Gregory Wheeler -- Research

Articles

Machine Epistemology and Big Data
The Routledge Companion to Philosophy of Social Science, forthcoming.

@inbook{BigData:2016,
title = {The Routledge Companion to Philosophy of Social Science},
editor = {Lee McIntyre and Alex Rosenberg},
publisher = {Routledge},
year = {2016},
author = {Gregory Wheeler},
chapter = {Machine Epistemology and Big Data}
}

[ bib| preprint]
Resolving Peer Disagreements Through Imprecise Probabilities (w/ Lee Elkin)
Noûs, forthcoming.

Two compelling principles, the Reasonable Range Principle and the Preservation of Irrelevant Evidence Principle, are necessary conditions that any response to peer disagreements ought to abide by. The Reasonable Range Principle maintains that a resolution to a peer disagreement should not fall outside the range of views expressed by the peers in their dispute, whereas the Preservation of Irrelevant Evidence (PIE) Principle maintains that a resolution strategy should be able to preserve unanimous judgments of evidential irrelevance among the peers. No conciliatory Bayesian resolution strategy satisfies the PIE Principle, however, and we give a sure loss argument in support of PIE and against Bayes. The theory of imprecise probability allows one to satisfy both principles, and we introduce the notion of a set-based credal judgment to frame and address a range of subtle issues that arise in peer disagreements.

@article{ip-peer:2015,
title = {Resolving Peer Disagreements Through Imprecise Probabilities},
author = {Lee Elkin and Gregory Wheeler},
journal = {No{\^{u}}s},
year = {forthcoming}
}

[abstract| bib| preprint]
Scoring Imprecise Credences: A Mildly Immodest Proposal (w/ Conor Mayo-Wilson)
Philosophy and Phenomenological Research 93(1): 55–78, 2016.

Jim Joyce argues for two amendments to probabilism. The first is the doctrine that credences are rational, or not, in virtue of their accuracy or "closeness to the truth" (Joyce 1998). The second is a shift from a numerically precise model of belief to an imprecise model represented by a set of probability functions (Joyce 2010). We argue that both amendments cannot be satisfied simultaneously. To do so, we employ a (slightly-generalized) impossibility theorem of Seidenfeld, Schervish, and Kadane (2012), who show that there is no strictly proper scoring rule for imprecise probabilities.
The question then is what should give way. Joyce, who is well aware of this no-go result, thinks that a quantifiability constraint on epistemic accuracy should be relaxed to accommodate imprecision. We argue instead that another Joycean assumption—called strict immodesty—should be rejected, and we prove a representation theorem that characterizes all "mildly" immodest measures of inaccuracy.

@article{IP-accuracy:2016,
title = {Scoring Imprecise Credences: A Mildly Immodest Proposal},
author = {Conor Mayo-Wilson and Gregory Wheeler},
journal = {Philosophy and Phenomenological Research},
year = {2016},
volume = {93},
number = {1},
pages = {55–78}
}

[abstract| bib| preprint]
Dilation, Disintegrations, and Delayed Decisions (w/ Arthur Paul Pedersen)
Proceedings of the 9th International Symposium on Imprecise Probability: Theories and Applications (ISIPTA 2015), Pescara, Italy: 227–236, 2015.

Both dilation and non-conglomerability have been alleged to conflict with a fundamental principle of Bayesian methodology that we call Good's Principle: one should always delay making a terminal decision between alternative courses of action if given the opportunity to first learn, at zero cost, the outcome of an experiment relevant to the decision. In particular, both dilation and non-conglomerability have been alleged to permit or even mandate choosing to make a terminal decision in deliberate ignorance of relevant, cost-free information. Although dilation and non-conglomerability share some simularities, some authors, including Walley and Seidenfeld, Schervish and Kadane, maintain that there are important differences between the two that warrant endorsing different normative positions regarding dilation (which is given a pass) and non-conglomerability (which is not). This article reassesses the grounds for treating dilation and non-conglomerability different. Our analysis exploits a new and general characterization result for dilation to draw a closer connection between dilation and non-conglomerability.

@inproceedings{isipta15_delayed-decisions:2015,
title = {Dilation, Disintegrations, and Delayed Decisions},
author = {Arthur Paul Pedersen and Gregory Wheeler},
booktitle = {Proceedings of the 9th International Symposium on Imprecise Probability: Theories and Applications},
address = {Pescara, Italy},
year = {2015},
pages = {227--236}
}

[abstract| bib| preprint]
Is there a Logic of Information?
Journal of Experimental and Theoretical Artificial Intelligence 27(1), 95–98, 2015.

Information-based epistemology maintains that 'being informed' is an independent cognitive state that cannot be reduced to knowledge or to belief, and the modal logic KTB has been proposed as a model. But what distinguishes the KTMB analysis of 'being informed', the Brouwersche schema, is precisely its downfall, for no logic of information should include (B) and, more generally, no epistemic modal should include (B), either.

@article{Wheeler.B:2015,
title = {Is there a Logic of Information?},
author = {Gregory Wheeler},
journal = {Journal of Experimental and Theoretical Artificial Intelligence},
year = {2015},
volume = {27},
number = {1},
pages = {95–98}
}

[abstract| bib| preprint| journal]

—— See also "Logic for Lunatics," Choice and Inference, August 20, 2013, [url]
Demystifying Dilation (w/ Arthur Paul Pedersen)
Erkenntnis 79(6), 1305–42, 2014.

Dilation occurs when an interval probability estimate of some event E is properly included in the interval probability estimate of E conditional on every event F of some partition, which means that one’s initial estimate of E becomes less precise no matter how an experiment turns out. Critics maintain that dilation is a pathological feature of imprecise probability models, while others have thought the problem is with Bayesian updating. However, two points are often overlooked: (1) knowing that E is stochastically independent of F (for all F in a partition of the underlying state space) is sufficient to avoid dilation, but (2) stochastic indepen- dence is not the only independence concept at play within imprecise probability models. In this paper we give a simple characterization of dilation formulated in terms of deviation from stochastic independence, propose a measure of dilation, and distinguish between proper and improper dilation. Through this we revisit the most sensational examples of dilation, which play up independence between dilator and dilatee, and find the sensationalism undermined by either fallacious reasoning with imprecise probabilities or improperly constructed imprecise probability models.

@article{PedWhe:2014,
title = {Coherence and Confirmation Through Causations},
author = {Arthur Paul Pedersen and Gregory Wheeler},
journal = {Erkenntnis},
year = {2014},
volume = {79},
number = {6},
pages = {1305–42}
}

[abstract| bib| preprint| journal]
Defeat Reconsidered and Repaired
The Reasoner 8(2), 15, 2014.

@article{Wheeler.defeat:2014,
title = {Defeat Reconsidered and Repaired},
author = {Gregory Wheeler},
journal = {The Reasoner},
year = {2014},
volume = {8},
pages = {3–4}
}

[ bib| preprint]
Character Matching and the Locke Pocket of Belief
Epistemology, Context, and Formalism, Franck Lihoreau and Manuel Rebuschi (Ed.), Dordrecht: The Synthese Library, Springer, pp. 185–94, 2014.

The Lockean thesis of full belief maintains that an individual believes a proposition just when he has a high enough level of confidence. The trouble with the Lockean thesis, according to probabilists like Richard Jeffrey, is that it licenses throwing away perfectly good information. Some proponents of the Lockean thesis---call them Harmonious Lockeans —maintain that reconciling qualitative and quantitative belief will need to occur on Jeffrey's terms. To this end, Scott Sturgeon has advanced a normative principle for Harmonious Lockeanism called Character Matching, which this essay criticizes through means of a counterexample and, with the help of a model of Henry Kyburg's, an alternative model for Harmonious Lockean belief that turns the Principle of Character Matching inside out. The upshot is that the character of evidence provides no corresponding normative constraint on the character of belief. A further consequence is that the disposition to fully believe, while dependent on a subject's practical interests, does not depend upon the total magnitude of the stake put at risk.

@inbook{Wheeler.CharacterMatch:2014,
title = {Character Matching and the Locke Pocket of Belief},
author = {Gregory Wheeler},
booktitle = {Epistemology, Context, and Formalism},
year = {2014},
editor = {Franck Lihoreau and Manuel Rebuschi},
address = {Dordrecht},
series = {The Synthese Library},
publisher = {Springer},
pages = {185–94}
}

[abstract| bib| preprint]
Coherence and Confirmation Through Causation (w/ Richard Scheines)
Mind 122(435), 135–70, 2013.

Coherentism maintains that coherent beliefs are more likely to be true than incoherent beliefs, and that coherent evidence provides more confirmation of a hypothesis when the evidence is made coherent by the explanation provided by that hypothesis. Although probabilistic models of credence ought to be well-suited to justifying such claims, negative results from Bayesian epistemology have suggested otherwise. In this essay we argue that the connection between coherence and confirmation should be understood as a relation mediated by the causal relationships among the evidence and a hypothesis, and we offer a framework for doing so by fitting together probabilistic models of coherence, confirmation, and causation. We show that the causal structure among the evidence and hypothesis is sometimes enough to determine whether the coherence of the evidence boosts confirmation of the hypothesis, makes no difference to it, or even reduces it. We also show that, ceteris paribus, it is not the coherence of the evidence that boosts confirmation, but rather the ratio of the coherence of the evidence to the coherence of the evidence conditional on a hypothesis.

@article{CCC:2013,
title = {Coherence and Confirmation Through Causation},
author = {Gregory Wheeler and Richard Scheines},
journal = {Mind},
year = {2013},
volume = {122},
number = {435},
pages = {135–70}
}

[abstract| bib| preprint| journal]
Models, Models, and Models
Metaphilosophy 44(3), 293–300, 2013.

Michael Dummett famously maintained that analytic philosophy was simply philosophy that followed Frege in treating the philosophy of language as the basis for all other philosophy (1978, 441). But one important insight to emerge from computer science is how difficult it is to animate the linguistic artifacts that the analysis of thought produces. Yet, modeling the effects of thought requires a new skill that goes beyond analysis: procedural literacy. Some of the most promising research in philosophy makes use of a variety of modeling techniques that go beyond basic logic and elementary probability theory. What unifies this approach is a focus on what Alan Perlis called procedural literacy. This essay argues that the future spoils in philosophical research will disproportionally go to those who are procedurally literate.

@article{Wheeler.models:2013,
title = {Models, Models, and Models},
author = {Gregory Wheeler},
journal = {Metaphilosophy},
year = {2013},
volume = {44},
number = {3},
pages = {293–300}
}

[abstract| bib| preprint| journal]
Objective Bayesian Calibration and the Problem of Non-convex Evidence
The British Journal for the Philosophy of Science 63(4), 841–850, 2012.

Jon Williamson's Objective Bayesian Epistemology relies upon a calibration norm to constrain credal probability by both quantitative and qualitative evidence. One role of the calibration norm is to ensure that evidence works to constrain a convex set of probability functions. This essay brings into focus a problem for Williamson's theory when qualitative evidence specifies non-convex constraints.

@article{Wheeler.calibration:2012,
title = {Objective Bayesian Calibration and the Problem of Non-convex Evidence},
author = {Gregory Wheeler},
journal = {The British Journal for the Philosophy of Science},
year = {2012},
volume = {63},
number = {4},
pages = {841–850}
}

[abstract| bib| preprint| journal]
Belief Contraction Through Safe Formulas (w/ Viktoriia Kozyreva)
Proceedings of the 14th International Workshop on Computer Science and Information Technologies, Hamburg - Ufa, Norwegian Fjords, 2012.

In this paper we consider approaches to belief revision and contraction in modal logics that are based on a translation of an agent’s beliefs in modal logic to first-order logic, where revision or contraction is performed before translating the result back into the original modal language. Contraction presents a unique problem, as theorems of the modal language can be accidentally removed, which would destroy the correspondence between a system of modal logic and its first-order simulation. We propose a solution for this problem based on defining safe-to-remove-parts of target formulas for contraction.

@inproceedings{KozWhe:2012,
title = {Belief Contraction Through Safe Formulas},
author = {Viktoriia Kozyreva and Gregory Wheeler},
booktitle = {Proceedings of the 14th International Workshop on Computer Science and Information Technologies},
year = {2012},
address = {Ufa-Hamburg-Norwegian Fjords},
}

[abstract| bib| preprint]
Why the Hardest Logic Puzzle Ever Cannot be Solved in Less Than Three Questions (w/ Pedro Barahona)
Journal of Philosophical Logic 41(1), 493–503, 2012.

Rabern and Rabern (2008) and Uzquiano (2010) have each presented increasingly harder versions of 'the hardest logic puzzle ever' (Boolos 1996), and each has provided a two-question solution to his predecessor's puzzle. But Uzquiano's puzzle is different from the original and different from Rabern and Rabern's in at least one important respect: it cannot be solved in less than three questions. In this paper we solve Uzquiano's puzzle in three questions and show why there is no solution in two. Finally, to cement a tradition, we introduce a puzzle of our own.

@article{WheBar:2012,
title = {Why the Hardest Logic Puzzle Ever Cannot be Solved in Less Than Three Questions},
author = {Gregory Wheeler and Pedro Barahona},
journal = {Journal of Philosophical Logic},
year = {2012},
issue = {41},
number = {1},
pages = {493–503}
}

[bib| preprint| journal]
—— Featured in New Scientist, December 2012.
Formal Epistemology
The Continuum Companion to Epistemology, Andrew Cullison (Ed.), pp. 227–47, 2012.

@inbook{Wheeler.fe:2012,
title = {Formal Epistemology},
author = {Gregory Wheeler},
booktitle = {The Continuum Companion to Epistemology},
year = {2011},
editor = {Andrew Cullison},
address = {New York},
publisher = {The Continuum Press},
pages = {227–47}
}

[bib| preprint]
Explaining the Limits of Olsson's Impossibility Result
The Southern Journal of Philosophy 50(1), 136–50, 2012.

In his groundbreaking book, Against Coherence (2005), Erik Olsson presents an ingenious impossibility theorem that appears to show that there is no informative relationship between probabilistic measures of coherence and higher likelihood of truth. Although Olsson’s result provides an important insight into probabilistic models of epistemological coherence, the scope of his negative result is more limited than generally appreciated. The key issue is the role conditional independence conditions play within the witness testimony model Olsson uses to establish his result. Olsson maintains that his witness model yields charitable ceteris paribus conditions for any theory of probabilistic coherence. Not so. In fact, Olsson’s model, like Bayesian witness models in general, selects a peculiar class of models that are in no way representative of the range of options available to coherence theorists. Recent positive results suggest that there is a way to develop a formal theory of coherence after all. Further, although Bayesian witness models are not conducive to the truth, they are conducive to reliability.

@article{Wheeler:2012,
title = {Explaining the Limits of Olsson's Impossibility Result},
author = {Gregory Wheeler},
journal = {The Southern Journal of Philosophy},
year = {2012},
volume = {50},
number = {1},
pages = {136--50}
}

[abstract| bib| preprint| journal]
Modeling of Phenomena and Dynamic Logic of Phenomena (w/ Boris Kovalerchuk and Leonid Perlovsky)
Journal of Applied Non-classical Logics 22(1), 51–82, 2012.

Modeling a complex phenomenon such as the mind presents tremendous computational complexity challenges. Modeling field theory (MFT) addresses these challenges in a non-traditional way. The main idea behind MFT is to match levels of uncertainty of the model (also, a problem or some theory) with levels of uncertainty of the evaluation criterion used to identify that model. When a model becomes more certain, then the evaluation criterion is adjusted dynamically to match that change to the model. This process is called the Dynamic Logic of Phenomena (DLP) for model construction and it mimics processes of the mind and natural evolution. This paper provides a formal description of DLP by specifying its syntax, semantics, and reasoning system. We also outline links between DLP and other logical approaches. Computational complexity issues that motivate this work are presented using an example of polynomial models.

@article{DLP:2012,
title = {Modeling of Phenomena and Dynamic Logic of Phenomena},
author = {Boris Kovalerchuk and Leonid Perlovsky and Gregory Wheeler},
journal = {Journal of Applied Non-classical Logics},
year = {2012},
volume = {22},
number = {1},
pages = {51–82}
}

[abstract| bib| preprint| journal]
NO Revision and NO Contraction (w/ Marco Alberti)
Minds and Machines 21(3), 411–30, 2011.

One goal of normative multi-agent system theory is to formulate principles for normative system change that maintain the rule-like structure of norms and preserve links between norms and individual agent obligations. A central question raised by this problem is whether there is a framework for norm change that is at once specific enough to capture this rule-like behavior of norms, yet general enough to support a full battery of norm and obligation change operators. In this paper we propose an answer to this question by developing a bimodal logic for norms and obligations called NO. A key to our approach is that norms are treated as propositional formulas, and we provide some independent reasons for adopting this stance. Then we define norm change operations for a wide class of modal systems, including the class of NO systems, by constructing a class of modal revision operators that satisfy all the AGM postulates for revision, and constructing a class of modal contraction operators that satisfy all the AGM postulates for contraction. More generally, our approach yields an easily extendable framework within which to work out principles for a theory of normative system change.

@article{WheAlb:2011,
title = {{NO} Revision and {NO} Contraction},
author = {Gregory Wheeler and Marco Alberti},
journal = {Minds and Machines},
year = {2011},
volume = {21},
number = {3},
pages = {411–30}
}

[abstract| bib| journal]
Evidential Probability and Objective Bayesian Epistemology (w/ Jon Williamson)
Handbook of the Philosophy of Statistics, Prasanta Bandyopadhyay and Malcom Forster (Eds.), pp. 376–92, 2011.

@inbook{WheWil:2011,
title = {Evidential Probability and Objective {B}ayesian Epistemology},
author = {Gregory Wheeler and Jon Williamson},
booktitle = {Handbook of the Philosophy of Statistics},
year = {2011},
editor = {Prasanta Bandyopadhyay and Malcom Forster},
address = {San Diego},
publisher = {North Holland Press},
pages = {307--331}
}

[bib| preprint| Amazon UK]
Focused Correlation, Confirmation, and the Jigsaw Puzzle of Variable Evidence (w/ Maximilian Schlosshauer)
Philosophy of Science 78(3), 376–92, 2011.

Focused correlation compares the degree of association within an evidence set to the degree of association in that evidence set given that some hypothesis is true. A difference between the confirmation lent to a hypothesis by one evidence set and the confirmation lent to that hypothesis by another evidence set is robustly tracked by a difference in focused correlations of those evidence sets on that hypothesis, provided that all the individual pieces of evidence are equally, positively relevant to that hypothesis. How- ever, that result depends on a very strong equal relevance condition on individual pieces of evidence. In this essay, we prove tracking results for focused correlation analogous to Wheeler and Scheines’s results but for cases involving unequal relevance. Our result is robust as well, and we retain conditions for bidirectional tracking between incre- mental confirmation measures and focused correlation.

@article{SchWhe:2011,
title = {Focused Correlation, Confirmation, and the Jigsaw Puzzle of Variable Evidence},
author = {Maximilian Schlosshauer and Gregory Wheeler},
journal = {Philosophy of Science},
year = {2011},
volume = {78},
number = {3},
pages = {376--92}
}

[abstract| bib| preprint| journal]
Causation, Association, and Confirmation (w/ Richard Scheines)
Explanation, Prediction, and Confirmation: New Trends and Olds Ones Reconsidered, D. Dieks, W.J. Gonzalez, S. Hartmann, T. Uebel, M. Weber (Eds.), Dordrecht: Springer, pp. 37–51, 2011.

Many philosophers of science have argued that a set of evidence that is "coherent" confirms a hypothesis which explains such coherence. In this paper, we examine the relationships between probabilistic models of all three of these concepts: coherence, confirmation, and explanation. For coherence, we consider Shogenji's measure of association (deviation from independence). For confirmation, we consider several measures in the literature, and for explanation, we turn to Causal Bayes Nets and resort to causal structure and its constraint on probability. All else equal, we show that focused correlation, which is the ratio of the coherence of evidence and the coherence of the evidence conditional on a hypothesis, tracks confirmation. We then show that the causal structure of the evidence and hypothesis can put strong constraints on how coherence in the evidence does or does not translate into confirmation of the hypothesis.

@inproceedings{fofs:2009,
title = {Causation, Association, and Confirmation},
author = {Gregory Wheeler and Richard Scheines},
booktitle = {Explanation, Prediction, and Confirmation: New Trends and Olds Ones Reconsidered},
editor ={Dennis Dieks and W.J. Gonzalez and Stephan Hartmann and Thomas Uebel and Marcel Weber},
year = {2011},
publisher = {Springer},
address = {Dordrecht},
pages = {37–51}
}

[abstract| bib| preprint| journal]
Editorial
Minds and Machines 21(1), 1–2, 2011.

@article{Wheeler.mm:2011,
title = {Editorial},
author = {Gregory Wheeler},
journal = {Minds and Machines},
year = {2011},
issue = {21},
number = {1},
pages = {1–2}
}

[bib| preprint| journal]
Robustness of Evidential Probability
The 16th International Conference on Logic for Programming, Artificial Intelligence, and Reasoning, Short Paper Proceedings, Dakar, Senegal, 2010.

Classical modal logics, based on the neighborhood semantics of Scott and Montague, provide a generalization of the familiar normal systems based on Kripke semantics. This paper defines AGM revision operators on several first-order monotonic modal correspondents, where each first-order correspondence language is defined by Marc Pauly’s version of the van Benthem characterization theorem for monotone modal logic. A revision problem expressed in a monotone modal system is translated into first-order logic, the revision is performed, and the new belief set is translated back to the original modal system. An example is provided for the logic of Risky Knowledge that uses modal AGM contraction to construct counter-factual evidence sets in order to investigate robustness of a probability assignment given some evidence set. A proof of correctness is given.

@inproceedings{Wheeler:2010,
title = {Robustness of Evidential Probability},
author = {Choh Man Teng and Gregory Wheeler},
editor = {Ed Clarke and Andrei Voronkov}
booktitle = {The 16th International Conference on Logic for Programming, Artificial Intelligence, and Reasoning (LPAR-16)},
year = {2010},
series = {Short paper proceedings},
note = {unpublished},
}

[abstract| bib| preprint]
AGM Belief Revision in Monotone Modal Logics
The 16th International Conference on Logic for Programming, Artificial Intelligence, and Reasoning, Short Paper Proceedings, Dakar, Senegal, 2010.

Evidential probability (EP) (Kyburg and Teng, 2001) assigns a probability to an event given a knowledge base containing statements about logical relationships of classes of objects as well as statements about statistical frequencies pertaining to some of those classes. While the focus of evidential probability is the assignment of probability to a particular event, we might ask about the robustness of the inference backing an assignment. Evaluating robustness is straightforward in most probabilistic logics, since propositions are interpreted with respect to a full joint distribution and thus each proposition may be manipulated individually. An EP knowledge base includes logical relationships as well as probabilistic relationships, so alterations of an EP knowledge base include a qualitative belief revision/contraction problem. The classical modal system EMN provides a qualitative representation of (EP) knowledge bases (Kyburg and Teng, 2002), and since many monotone neighborhood structures may be simulated by bi-modal Kripke structures that admit a first-order correspondent, AGM revision and contraction operators are definable with respect to this (indirect) first-order correspondence. Specifically, system EMN has a first-order correspondent on which AGM revision and contraction operators are defined. Robustness of an EP assignment to a statement is a function of the variation of EP assignment to that event across varying evidence, where varying evidence is represented by a class of different contractions. Conditions and measures of robustness are proposed and discussed.

@inproceedings{Wheeler:2010,
title = {AGM Belief Revision in Monotone Modal Logics},
author = {Gregory Wheeler},
editor = {Ed Clarke and Andrei Voronkov}
booktitle = {The 16th International Conference on Logic for Programming, Artificial Intelligence, and Reasoning (LPAR-16)},
year = {2010},
series = {Short paper proceedings},
note = {unpublished},
}

[abstract| bib| preprint]
AGM Belief Revision in Monotone Modal Logics
The 16th International Conference on Logic for Programming, Artificial Intelligence, and Reasoning, Short Paper Proceedings 2010.

Classical modal logics, based on the neighborhood semantics of Scott and Montague, provide a generalization of the familiar normal systems based on Kripke semantics. This paper defines AGM revision operators on several first-order monotonic modal correspondents, where each first-order correspondence language is defined by Marc Pauly’s version of the van Benthem characterization theorem for monotone modal logic. A revision problem expressed in a monotone modal system is translated into first-order logic, the revision is performed, and the new belief set is translated back to the original modal system. An example is provided for the logic of Risky Knowledge that uses modal AGM contraction to construct counter-factual evidence sets in order to investigate robustness of a probability assignment given some evidence set. A proof of correctness is given.

@inproceedings{Wheeler:2010,
title = {AGM Belief Revision in Monotone Modal Logics},
author = {Gregory Wheeler},
booktitle = {The 16th International Conference on Logic for Programming, Artificial Intelligence, and Reasoning (LPAR-16)},
year = {2009},
series = {Short paper proceedings},
note = {unpublished},
}

[abstract| bib| preprint]
Focused Correlation and Confirmation
The British Journal for the Philosophy of Science 60(1), 79–100, 2009.

This essay presents results about a deviation from independence measure called focused correlation. This measure explicates the formal relationship between probabilistic de- pendence of an evidence set and the incremental confirmation of a hypothesis, resolves a basic question underlying Peter Klein and Ted Warfield’s ‘truth-conduciveness’ problem for Bayesian coherentism, and provides a qualified rebuttal to Erik Olsson’s claim that there is no informative link between correlation and confirmation. The generality of the result is compared to recent programs in Bayesian epistemology that attempt to link correlation and confirmation by utilizing a conditional evidential independence condition. Several properties of focused correlation are also highlighted.

@article{Wheeler:2009,
title = {Focused Correlation and Confirmation},
author = {Gregory Wheeler},
journal = {The British Journal for the Philosophy of Science},
year = {2009},
volume = {60},
number = {1},
pages = {79--100}
}

[abstract| bib| preprint| journal]
A Good Year for Imprecise Probabilities
Commissioned in 2009 for PHIBOOK, Vincent F. Hendricks (Ed.), VIP / Automatic Press. 49–79; forthcoming.

@unpublished{Wheeler.IP:2009,
title = {A Good Year for Imprecise Probabilities},
author = {Gregory Wheeler},
booktitle = {A Good Year for Imprecise Probabilities},
year = {2009}
}

[ bib| preprint]
Logical Relations in a Statistical Problem (w/ Jan-Willem Romeijn, Rolf Haenni, and Jon Williamson)
Foundations of the Formal Sciences, London: College Publications, pp. 49–79, 2009.

This paper presents the progicnet programme. It proposes a general framework for probabilistic logic that can guide inference based on both logical and probabilistic input, and it introduces a common calculus for making inferences in the framework. After an introduction to the programme as such, it is illustrated by means of a toy example from psychometrics. It is shown that the framework and calculus can accommodate a number of approaches to probabilistic reasoning: Bayesian statistical inference, evidential probability, probabilistic argumentation, and objective Bayesianism. The progicnet programme thus provides insight into the relations between these approaches, it illustrates how the results of different approaches can be combined, and it provides a basis for doing efficient inference in each of the approaches.

@inproceedings{fofs:2009,
title = {Logical Relations in a Statistical Problem},
author = {Jan-Willem Romeyn and Rolf Haenni and Gregory Wheeler and Jon Williamson},
booktitle = {Foundations of the Formal Sciences VI: Reasoning about Probabilities and Probabilistic Reasoning},
year = {2009},
series = {Studies in Logic},
publisher = {College Publications},
address = {London},
pages = {49–79}
}

[abstract| bib| preprint]
Review of Hendricks and Symons' Formal Philosophy
Philosophy of Science 76(1), 113–5, 2009.

@article{Wheeler.FP-Review:2005,
title = {Review of Hendricks and Symons' {\emph Formal Philosophy}},
author = {Gregory Wheeler},
journal = {Philosophy of Science},
year = {2009},
issue = {76},
number = {1},
pages = {113–5}
}

[bib| preprint| journal]
Methodological Naturalism and Epistemic Internalism (w/ Luís Moniz Pereira)
Synthese 163(3), 315–28, 2008.

Epistemic naturalism holds that the results or methodologies from the cognitive sciences are relevant to epistemology, and some have maintained that scien- tific methods are more compatible with externalist theories of justification than with internalist theories. But practically all discussions about naturalized epistemology are framed exclusively in terms of cognitive psychology, which is only one of the cognitive sciences. The question addressed in this essay is whether a commitment to naturalism really does favor externalism over internalism, and we offer reasons for thinking that naturalism in epistemology is compatible with both internalist and externalist concep- tions of justification. We also argue that there are some distinctively internalist aims that are currently being studied scientifically and these notions, and others, should be studied by scientific methods.

@article{WhePer:2008,
title = {Methodological Naturalism and Epistemic Internalism},
author = {Gregory Wheeler and Lu\'{i}s Moniz Pereira},
journal = {Synthese},
year = {2008},
volume = {163},
number = {3},
pages = {315–28}
}

[abstract| bib| preprint| journal]
Possible Semantics for a Common Framework for Probabilistic Logic (w/ Rolf Haenni, Jan-Willem Romeijn, and Jon Williamson)
International Workshop on Interval Probabilistic Uncertainty and Non-Classical Logics (UncLog'08), V. N. Huynh (Ed.), Ishikawa Japan, Advances in Soft Computing Series, 268-79, 2008.

This paper proposes a common framework for various probabilistic logics. It consists of a set of uncertain premises with probabilities attached to them. This raises the question of the strength of a conclusion, but without imposing a particular seman- tics, no general solution is possible. The paper discusses several possible semantics by looking at it from the perspective of probabilistic argumentation.

@inproceedings{Wheeler:2008,
title = {Possible Semantics for a Common Framework of Probabilistic Logics},
author = {Rolf Haenni and Jan-Willem Romeyn and Gregory Wheeler and Jon Williamson},
booktitle = {International Workshop on Interval Probabilistic Uncertain and Non-classical Logics},
editor = {V. N. Huynh},
year = {2008},
series = {Advances in Soft Computing},
pages = {268–79}
}

[abstract| bib| preprint| proceedings]
Applied Logic without Psychologism
Studia Logica 88(1), 137–56, 2008.

Logic is a celebrated representation language because of its formal generality. But there are two senses in which a logic may be considered general, one that concerns a technical ability to discriminate between different types of individuals, and another that concerns constitutive norms for reasoning as such. This essay embraces the former, permutation-invariance conception of logic and rejects the latter, Fregean conception of logic. The question of how to apply logic under this pure invariantist view is addressed, and a methodology is given. The pure invariantist view is contrasted with logical pluralism, and a methodology for applied logic is demonstrated in remarks on a variety of issues concerning non-monotonic logic and non-monotonic inference, including Charles Morgan's impossibility results for non-monotonic logic, David Makinson's normative constraints for non-monotonic inference, and Igor Douven and Timothy Williamson's proposed formal constraints on rational acceptance.

@article{Wheeler:2008,
title = {Applied Logic without Psychologism},
author = {Gregory Wheeler},
journal = {Studia Logica},
year = {2008},
volume = {88},
number = {1},
pages = {137–56}
}

[abstract| bib| preprint]
Conditionals and Consequences (w/ Henry Kyburg and Choh Man Teng)
Journal of Applied Logic 5(4), 638–50, 2007.

We examine the notion of conditionals and the role of conditionals in inductive logics and arguments. We identify three mistakes commonly made in the study of, or motivation for, non-classical logics. A nonmonotonic consequence relation based on evidential probability is formulated. With respect to this acceptance relation some rules of inference of System P are unsound, and we propose refinements that hold in our framework.

@article{KTW:2007,
title = {Conditionals and Consequences},
author = {Henry E. Kyburg, Jr. and Choh Man Teng and Gregory Wheeler},
journal = {Journal of Applied Logic},
year = {2007},
volume = {5},
number = {4},
pages = {638–50}
}

[abstract| bib| preprint]
Two Puzzles Concerning Measures of Uncertainty and the Positive Boolean Connectives
13th Portuguese Conference on Artificial Intelligence (EPIA 2007), LNAI Series, Berlin: Springer-Verlag, 170-80, 2007.

The two puzzles are the Lottery Paradox and the Amalgamation Paradox, which both point out difficulties for aggregating uncertain information. A generalization of the lottery paradox is presented and a new form of an amalgamation reversal is introduced. Together these puzzles highlight a difficulty for introducing measures of uncertainty to a variety of logical knowledge representation frameworks. The point is illustrated by contrasting the constraints on solutions to each puzzle with the structural properties of the preferential semantics for non-monotonic logics (System P), and also with systems of normal modal logics. The difficulties illustrate several points of tensions between the aggregation of uncertain information and aggregation according to the monotonically positive Boolean connectives, ∧ and ∨.

@inproceedings{Wheeler:2007,
title = {Two Puzzles Concerning Measures of Uncertainty and the Positive Boolean Connectives},
author = {Gregory Wheeler},
booktitle = {13th Portuguese Conference on Artificial Intelligence (EPIA 2007)},
publisher = {Springer},
year = {2007},
series = {LNAI},
address = {Berlin},
pages = {170–80}
}

[abstract| bib| preprint| proceedings]
A Review of the Lottery Paradox
In Probability and Inference: Essays in Honour of Henry E. Kyburg, Jr., William Harper and Gregory Wheeler (Eds.), London: King's College Publications, pp. 1-31, 2007.

@inbook{Wheeler.lottery:2007,
title = {A Review of the Lottery Paradox},
author = {Gregory Wheeler},
booktitle = {Probability and Inference: Essays in Honor of {H}enry {E}. {K}yburg, {J}r.},
publisher = {King's College Publications},
year = {2007},
address = {London},
pages = {1–31}
}

[ bib| preprint]
Humanists and Scientists
The Reasoner 1(1), 3–4, 2007.

@article{Wheeler:2007,
title = {Humanists and Scientists},
author = {Gregory Wheeler},
journal = {The Reasoner},
year = {2007},
volume = {1},
pages = {3–4}
}

[ bib| preprint]
Rational Acceptance and Conjunctive/Disjunctive Absorption
Journal of Logic, Language and Information 15(1-2): 49-63, 2006.

A bounded formula is a pair consisting of a propositional formula φ in the first coordinate and a real number within the unit interval in the second coordinate, interpreted to express the lower-bound probability of φ. Converting conjunctive/disjunctive combinations of bounded formulas to a single bounded formula consisting of the conjunction/disjunction of the propositions occurring in the collection along with a newly calculated lower probability is called absorption. This paper introduces two inference rules for effecting conjunctive and disjunctive absorption and compares the resulting logical system, called System Y, to axiom System P. Finally, we demonstrate how absorption resolves the lottery paradox and the paradox of the preference.

@article{Wheeler:2006,
title = {Rational Acceptance and Conjunctive/Disjunctive Absorption},
author = {Gregory Wheeler},
journal = {Journal of Logic, Language, and Information},
year = {2006},
volume = {15},
number = {1–2},
pages = {49–63}
}

[abstract| bib| preprint| journal]
On the Structure of Rational Acceptance: Comments on Hawthorne and Bovens
Synthese 144(2), 287–304, 2005.

The structural view of rational acceptance is a commitment to developing a logical calculus to express rationally accepted propositions sufficient to represent valid argument forms constructed from rationally accepted formulas. This essay argues for this project by observing that a satisfactory solution to the lottery paradox and the paradox of the preface calls for a theory that both (i.) offers the facilities to represent accepting less than certain propositions within an interpreted artificial language and (ii) provides a logical calculus of rationally accepted formulas that preserves rational acceptance under consequence. The essay explores the merit and scope of the structural view by observing that some limitations to a recent framework advanced James Hawthorne and Luc Bovens are traced to their framework satisfying the first of these two conditions but not the second.

@article{Wheeler:2005,
title = {On the Structure of Rational Acceptance: Comments on Hawthorne and Bovens},
author = {Gregory Wheeler},
journal = {Synthese},
year = {2005},
volume = {144},
number = {2},
pages = {287–304}
}

[abstract| bib| preprint| journal]
—— Reprinted in Knowledge, Rationality and Action, Wiebe van der Hoek (Ed.), Dordrecht: Springer, 117-34, 2006.
Review of Hans Rott's Change, Choice, and Inference: A Study of Belief Revision and Nonmonotonic Reasoning
Philosophy of Science 72(3), 498-503, 2005.

This essay proposes to resolve the lottery paradox and the paradox of the preface within the framework of a non-monotonic logic called Statistical Default Logic, yielding a solution to the two paradoxes that falls within the tradition of restricting closure operations on rationally accepted propositions. The essay advances a structural view of the paradoxes, one that holds that a solution to the paradoxes must (i) offer a scheme for representing accepting less than certain propositions and (ii) provide a logic that preserves acceptance under entailment.

@article{Wheeler.RottReview:2005,
title = {Review of Hans Rott's {\emph Change, Choice and Inference: A Study of Belief Revision and Nonmonotonic Reasoning}},
author = {Gregory Wheeler},
journal = {Philosophy of Science},
year = {2005},
issue = {72},
number = {3},
pages = {498–503}
}

[preprint| journal]
The Paradoxes of Rational Acceptance and the Logic of Belief
In Computing, Philosophy and Cognition, Lorenzo Magnani and Riccardo Dossena (Eds.), London: King's College Publications, 417–32, 2005.

This essay proposes to resolve the lottery paradox and the paradox of the preface within the framework of a non-monotonic logic called Statistical Default Logic, yielding a solution to the two paradoxes that falls within the tradition of restricting closure operations on rationally accepted propositions. The essay advances a structural view of the paradoxes, one that holds that a solution to the paradoxes must (i) offer a scheme for representing accepting less than certain propositions and (ii) provide a logic that preserves acceptance under entailment.

@inbook{Wheeler:2005,
title = {The Paradoxes of Rational Acceptance and the Logic of Belief},
author = {Gregory Wheeler},
booktitle = {Computing, Philosophy, and Cognition},
editor = {Lorenzo Magnani and Riccardo Dossena},
year = {2005},
publisher = {King's College Publications},
address = {London},
pages = {417–32} }

[abstract| bib]
Epistemology and Artificial Intelligence (w/ Luís Moniz Pereira)
Journal of Applied Logic 2(4), 469–93, 2004

In this essay we advance the view that analytical epistemology and artificial intelligence are complementary disciplines. Both fields study epistemic relations, but whereas artificial intelligence approaches this subject from the perspective of understanding formal and computational properties of frameworks purporting to model some epistemic relation or other, traditional epistemology ap- proaches the subject from the perspective of understanding the properties of epistemic relations in terms of their conceptual properties. We argue that these two practices should not be conducted in isolation. We illustrate this point by discussing how to represent a class of inference forms found in standard inferential statistics. This class of inference forms is interesting because its members share two properties that are common to epistemic relations, namely defeasibility and paraconsistency. Our modeling of standard inferential statistical arguments exploits results from both logical artificial intelligence and analytical epistemology. We remark how our approach to this modeling problem may be generalized to an interdisciplinary approach to the study of epistemic relations.

@article{WhePer:2004,
title = {Epistemology and Artificial Intelligence},
author = {Gregory Wheeler and Lu\'{i}us Moniz Pereira},
journal = {Journal of Applied Logic},
year = {2004},
volume = {2},
number = {4},
pages = {469–93} }

[abstract| bib| preprint| journal]
An Implementation of Statistical Default Logic (w/ Carlos Damásio)
In Logics in Artificial Intelligence (JELIA 2004), José Alferes and João Leite (Eds.), LNAI Series, Berlin: Springer-Verlag, 121-33, 2004.

Statistical Default Logic (SDL) is an expansion of classical (i.e., Reiter) default logic that allows us to model common inference patterns found in standard inferential statistics, e.g., hypothesis testing and the estimation of a population‘s mean, variance and proportions. This paper presents an embedding of an important subset of SDL theo- ries, called literal statistical default theories, into stable model semantics. The embedding is designed to compute the signature set of literals that uniquely distinguishes each extension on a statistical default theory at a pre-assigned error-bound probability.

@inproceedings{WheDam:2004,
title = {An Implementation of Statistical Default Logic},
author = {Gregory Wheeler and Carlos Dama\'{a}sio},
booktitle = {Logics in Artificial Intelligence},
year = {2004},
pages = {121–133},
editor = José Alferes and João Leite},
series = {Lecture Notes in Artificial Intelligence}
volume = {3229},
publisher = {Springer},
address = {Berlin}
}

[abstract| bib| preprint| proceedings]
A Resource Bounded Default Logic
In Proceedings of the 10th International Workshop on Non-Monotonic Reasoning (NMR 2004), James Delgrande and Torsten Schaub (Eds.) Whistler, British Columbia, 416-22, 2004.

This paper presents statistical default logic, an expansion of classical (i.e., Reiter) default logic that allows us to model common inference patterns found in standard inferential statistics, including hypothesis testing and the estimation of a population’s mean, variance and proportions. The logic replaces classical defaults with ordered pairs consisting of a Reiter default in the first coordinate and a real number within the unit interval in the second coordinate. This real number represents an upper-bound limit on the probability of accepting the consequent of an applied default and that consequent being false. A method for constructing extensions is then defined that preserves this upper bound on the probability of error under a (skeptical) non-monotonic consequence relation.

@inproceedings{Wheeler:2004,
title = {A Resource Bounded Default Logic},
author = {Gregory Wheeler},
booktitle = {Proceedings of the 10th International Workshop on Non-Monotonic Reasoning (NMR 2004)},
year = {2004},
pages = {416–422},
editor = {James Delgrande and Torsten Schaub},
publisher = {AAAI Press},
address = {Whistler, British Columbia}
}

[abstract| bib| preprint]

—— An abstract appears in The Bulletin of Symbolic Logic, 10(3): 444, 2004.
A Note on Epistemology and Logical Artificial Intelligence (w/ Luís Moniz Pereira)
In Proceedings of the Third International Workshop on Computational Models of Scientific Reasoning and Applications (CMSRA-III), Buenos Aires, Argentina, 207-22, 2003.

Contemporary analytical epistemology and logical artificial intelligence are complementary disciplines. This is most apparent when considering the structure of what we call {epistemic relations, among which inferential are of special concern. In this essay we discuss key correspondence results between semantics for logic programs and default logic. Our aim is to show that there now exist sufficient theoretical foundations within logical artificial intelligence to warrant use of non-monotonic logics as analytical tools within the theory of knowledge.

@inproceedings{Wheeler.esslli:2002,
title = {Statistical Defaults and Paraconsistency},
author = {Gregory Wheeler and Luís Moniz Pereira},
booktitle = {Proceedings of the Third International Workshop on Computational Models of Scientific Reasoning and Applications},
year = {2003},
address = {Buenos Aires, Argentina}
}

[abstract| bib]

—— An expanded version appears in The Journal of Applied Logic 2(4), 2004.
Statistical Defaults and Paraconsistency
In ESSLLI Workshop on Paraconsistent Logic (ESSLLI 2002), Trento, Italy. CLE e-Prints, vol. 2(2), Campinas, Brazil, 2002.

This paper discusses the relationship between the property of paraconsistency and Statistical Default Logic, a nonmonotonic logic that models common inference forms found in classical statistical inference such as hypothesis testing and the estimation of a population's mean, variance and proportions. Statistical Default Logic is paraconsistent in the sense that a set of default inference forms may induce an inconsistent set of conclusions yet not, by that fact alone, trivialize the statistical default consequence relation. The paper also clarifies a distinction between the studies of implication, reasoning and inference. This distinction is useful for understanding how to evaluate statistical defaults vis a vis probabilistic approaches to statistical argumentation and, it is suggested, useful for evaluating non-standard logics.

@inproceedings{Wheeler.esslli:2002,
title = {Statistical Defaults and Paraconsistency},
author = {Gregory Wheeler},
booktitle = {ESSLLI Workshop on Paraconsistent Logic},
publisher = {CLE e-Prints},
year = {2002},
volume = {2},
number = {2},
address = {Campinas, Brazil},
issn = {1519–9681} }

[abstract| bib]
Kinds of Inconsistency
In Paraconsistency, Walter A. Carnielli, Marcelo E. Coniglio, and Italia Loffredo D'Ottaviano (Eds.), New York: Marcel Dekker, 511–22, 2002.

Typically paraconsistency is motivated by one of two types of arguments: either an ontological argument is given whereby it is claimed that inconsistent objects or events of some kind demand a logic able to reason about such items, or an epistemological argument is provided that denies that language or the world is infected with inconsistency but claims instead that the problem is all in a reasoning agent's head. Approaches to designing paraconsistent logics have thus far tended to heed this distinction. Stronger, dialetheic logics are called on to handle contradictory objects or events in a manner that does not trivialize inference, while these logics are out of favor with epistemological approaches which favor preserving as much of classical logic as possible. This latter approach is typically viewed as one of introducing a set of techniques for how to manipulate an agent's inconsistent yet rational corpus to preserve a familiar form of logical consequence. This essay argues against the practice of linking epistemological concerns with weak paraconsistent logics. It introduces an epistemological motivation for adopting a strong paraconsistent logic by considering the results of measuring physical objects and how we might go about reasoning with these results. Measurement behaves in a way as to be a source of inconsistency that is neither best understood as a problem between agents nor the result of either a paradoxical property of language or the world.

@inbook{Wheeler:2002,
title = {Kinds of Inconsistency},
author = {Gregory Wheeler},
booktitle = {Paraconsistency},
publisher = {Marcel Dekker},
year = {2002},
editor = {Walter A. Carnielli and Marcelo E. Coniglio and Italia Loffredo D'Ottaviano},
volume = {228},
series = {Lecture Notes in Pure and Applied Mathematics},
pages = {410–420},
address = {New York}
}

[abstract| bib]
Error Statistics and Duhem's Problem
Philosophy of Science 67(3), 410–20, 2000.

No one has a well developed solution to Duhem's problem, the problem of how experimental evidence warrants revision of our theories. Deborah Mayo proposes a solution to Duhem's problem in route to her more ambitious program of providing a philosophical account of inductive inference and experimental knowledge. This paper is a response to Mayo's Error Statistics (ES) program, paying particular attention to her response to Duhem's problem. It turns out that Mayo's purported solution to Duhem's problem is very significant to her project, for the epistemic license claimed by ES and the philosophical underpinnings to her account of experimental knowledge depend on this solution. By introduction the partition problem, I argue that ES fails to solve Duhem's problem and therefore fails to provide an adequate account of experimental knowledge.

@article{Wheeler:2000,
title = {Error Statistics and Duhem's Problem},
author = {Gregory Wheeler},
journal = {Philosophy of Science},
year = {2000},
volume = {67},
pages = {410–420}
}

[abstract| bib| preprint| journal]

Monograph

2011: Probabilistic Logics and Probabilistic Networks
Rolf Haenni, Jan-Willem Romeijn, Gregory Wheeler, and Jon Williamson.
The Synthese Library, Springer.
Available from Amazon: UK or US.

- Reviewed by Jan Sprenger in Metascience.

Edited Books

2013: New Challenges to Philosophy of Science
Hanne Andersen, Dennis Dieks, Wenceslao González, Marcel Weber, and Gregory Wheeler (eds) The Philosophy of Science in a European Perspective Series, Dordrecht: Springer.
Available from Amazon: UK or US
2007: Probability and Inference: Essays in Honour of Henry E. Kyburg, Jr.
William Harper and Gregory Wheeler, (eds.)
London: College Publications, 2007.
Available from Amazon: UK or US.

Special Journal Issues

2012: "Special issue Commemorating Henry E. Kyburg, Jr.," Synthese, volume 186, number 2. (co-edited w/ Horacio Arló-Costa)
2009: “Special issue on Combining Probability and Logic”, The Journal of Applied Logic, volume 7, number 2. (w/ Fabio Cozman, Rolf Haenni, Jan-Willem Romeijn, and Jon Williamson.)
2007: “Special issue on Formal and Computational Epistemology,” The Journal of Applied Logic, volume 5, number 4. (w/ Luís Moniz Pereira)

Recent Projects

Deutscher Akademischer Austausch Dienst / German Academic Exchange Service (DAAD): The Puzzle of Heuristic Rationality, with Konstantinos Katsikopoulos
The Max Planck Institute for Human Development, Berlin (2012).
European Science Foundation (ESF), LogiCCC Program: Dialogical Foundations of Semantics, (DiFoS), associate partner, (2009-2011).
European Science Foundation (ESF): Philosophy of Science in a European Perspective (PSE), formal methods group & steering committee, (2008-2013).
The Leverhulme Trust: Probabilistic Logics and Probabilistic Networks PROGICNET. co-PI, (2006-2008).

Collaborators

Marco Alberti (New University of Lisbon)
Pedro Barahona (New University of Lisbon)
Carlos Damásio (New University of Lisbon)
Lee Elkin (Munich)
Rolf Haenni (Bern)
Konstantinos Katsikopoulos (Max Planck Institute for Human Development)
Boris Kovalerchuk (Central Washington University)
Viktoriia Kozyreva, (Ufa State Aviation Technical University)
Henry E. Kyburg, Jr.* (Rochester)
Conor Mayo-Wilson (University of Washington)
Arthur Paul Pedersen (Regensburg)
Luís Moniz Pereira (New University of Lisbon)
Leonid Perlovsky (Harvard)
Jan-Willem Romeijn (Groningen)
Richard Scheines (Carnegie Mellon)
Maximillian Schlosshauer (Copenhagen)
Choh Man Teng (Institute for Human and Machine Cognition)
Jon Williamson (Kent)

Co-editors

Hanne Andersen (Aarhus)
Horacio Arló-Costa* (Carnegie Mellon)
Fabio Cozman (São Paulo)
Dennis Dieks (Utrecht)
Wenceslao González (Coruña)
William Harper (Western Ontario)
Marcel Weber (Geneva)

Articles

Monograph

Edited Books

Special Journal Issues

Recent Projects

Collaborators

Co-editors

Erdös Number