Workshop on Simplicity and Causal Discovery

June 7-8, 2014, at Carnegie Mellon University. Stay tuned.

Modal Logic Workshop: Consistency and Structure


8:30 AM, Saturday, April 12, 2014, Wean Hall 4625, Carnegie Mellon University.


8:30-9:00 Bagels and coffee

Session I: Consistency

9:00-10:30 The Paradox of the Two Firemen
J. Michael Dunn, School of Informatics & Computing, and Dept. of Philosophy, Indiana University Bloomington

10:45-12:00 Clean Epistemic Principles from Messy Belief
Kevin T. Kelly, Dept. of Philosophy, Carnegie Mellon University

12:00-2:00 Lunch

Session II: Structure:

2:00-3:30 Partiality and Adjointness in Modal Logic,
Wesley Holliday, Dept. of Philosophy, University of California, Berkeley

3:45-5:00 Topos theoretic semantics for higher-order modal logic
Steven Awodey, Dept. of Philosophy, Carnegie Mellon University.

5:00-6:30 Topological Semantics for Provability Logics
Thomas Icard, Herbert Simon Postdoctoral Fellow, Carnegie Mellon University, Department of Philosophy, Stanford Univesity.


The Paradox of the Two Firemen
J. Michael Dunn, School of Informatics & Computing, and Dept. of Philosophy, Indiana University Bloomington

Click for abstract

Bar-Hillel and Carnap (1953, p. 229)) wrote: "It might perhaps, at first, seem strange that a self-contradictory sentence, hence one which no ideal receiver would accept, is regarded as carrying with it the most inclusive information. ... A self-contradictory sentence asserts too much; it is too informative to be true." Floridi (2011) has dubbed this Bar-Hillel-Carnap Paradox. If an agent can have inconsistent beliefs, this poses obvious problems for logics of belief based on classical modal logic if they are not to be mere idealizations. Various paraconsistent logicians (including myself) have argued for theories of information wherein different contradictions could contain different amounts of information. But the Paradox of the Two Firemen below occurred to me only recently. I am embarrassed to admit this except for the fact that the phenomenon it represents seems not to have been discussed in the literature surrounding contradictions.

Suppose you are awakened in your hotel room on the 30th floor by a fire alarm. Your look around you and your room is on fire. You open the door. You see three possible ways out: left, right, straight ahead.

Scenario 1. You see two apparently experienced and well-intentioned firemen. One says there is exactly one safe route and it is to your left. The other says there is exactly one safe route and it is to your right. Contradictory information!

Scenario 2. You find no one to give directions. Incomplete information! Nothing! Question: Which scenario would you prefer?

I think it is obvious that a rational agent would prefer to be in Scenario 1. While the two firemen are giving you contradictory information, they are also both giving you the useful information that there is a safe way out and it is not straight ahead. It appears that three choices have been reduced to two, thereby increasing your odds for survival. Now you have to pick from those two and run, hoping to find the exit.

In my talk I shall consider various reactions to the Paradox of the Two Firemen and defend that it is an example of contradictory information being better than nothing (and relevant to decision making).

My own preferred reaction is related to my CMU Philosophy Colloquium earlier this week, and is based on "Contradictory Information: Too Much of a Good Thing" (Dunn (2009)), where I embedded the "Belnap-Dunn 4-valued Logic" (Truth, Falsity, Neither, Both) into a context of subjective probability generalized to allow for degrees of belief, disbelief, and two kinds of uncertainty --- that in which the reasoner has too little information (ignorance) and that in which the reasoner has too much information (conflict). Jøsang's (1997) "Opinion Triangle" was thus expanded to an "Opinion Tetrahedron" with the 4-values as its vertices. I shall explain how this can be used to resolve the Paradox of the Two Firemen.

REFERENCES: J. Michael Dunn (2009), "Contradictory Information: Too Much of a Good Thing," Journal of Philosophical Logic, 39, 425-452; Yehoshua Bar-Hillel and Rudolf Carnap (1953), "Semantic Information." The British Journal for the Philosophy of Science, 4, 147-157; Luciano Floridi (2011), The Philosophy of Information, Oxford University Press; A. Jøsang (1997), "Artificial Reasoning with Subjective Logic," Proceedings of the Second Australian Workshop on Commonsense Reasoning, Perth.

Clean Epistemic Principles From Messy Belief
Kevin T. Kelly, Dept. of Philosophhy, Carnegie Mellon University

Click for abstract

The beliefs of computationally bounded agents like ourselves are a logical mess. They are not even remotely consistent, deductively closed, or rationally revised. It appears hopeless to validate any interesting epistemological principles for such messy belief states, so the usual response is to impose idealizations upon belief prior to seeking generally valid principles of knowledge. To the contrary, I present a computationally grounded semantics for empirical knowledge in which S4-like principles are valid for knowledge, assuming no idealizations whatever concerning belief. The idea is to model knowledge as the culmination of empirical inquiry and to interpret theses of epistemic logic as assertions of conditional cognitive feasibility. The proposed semantics explains how empirical knowledge can survive massive inconsistency, why empirical knowledge does not require a logic of discovery, how common knowledge can emerge in a population, and even how it is possible to know one's own Moore sentence. Cf: Kevin T. Kelly, "A Computational Learning Semantics for Inductive Empirical Knowledge',Logical/Informational Dynamics, a Festschrift for Johan van Benthem, A. Baltag and S. Smets eds., Springer: 2014.

Partiality and Adjointness in Modal Logic
Wesley Holliday, Dept. of Philosophy, University of California, Berkeley

Click for abstract

Following a proposal of Lloyd Humberstone ("From Worlds to Possibilities," Journal of Philosophical Logic, 1981), in this talk I will discuss semantics for modal logic based on partial possibilities rather than total worlds. As I will show, a fascinating feature of a semantics along these lines is that for each member of a standard family of normal modal logics, one can build a canonical possibility model, wherein every logically consistent formula is satisfied, out of the lattice of formulas related by provable implication in the logic. The states in such a canonical possibility model are individual finite formulas, rather than infinite maximally consistent sets of formulas as in standard canonical world models. Constructing these "locally finite" canonical models involves first solving a problem in pure modal logic of independent interest, related to the study of adjoint pairs of modal operators: for a given modal logic L, is there a function F_L on the set of formulas such that for all formulas phi and psi, the implication phi --> BOX psi is provable in L if and only if the implication F_L(phi) --> psi is provable in L? I answer this question for a standard family of normal modal logics, using model-theoretic arguments involving world semantics. Time permitting, I will conclude with a survey of other results relating possibility models and world models. A manuscript containing this material is available upon request at

Topos theoretic semantics for higher-order modal logic
Steven Awodey, Dept. of Philosophy, Carnegie Mellon University.

Click for abstract

We define the notion of a model of higher-order modal logic in an arbitrary elementary topos.  In contrast to the well-known interpretation of (non-modal)  higher-order logic, the type of propositions is not interpreted by the subobject classifier of the topos, but by a suitable complete Heyting algebra. The canonical map relating the two then serves to interpret equality and provides a modal operator, in the form of a comonad. Examples of such structures arise from continuous maps of spaces. The usual Kripke, neighborhood, and sheaf semantics for propositional and first-order modal logic are subsumed by this notion.

Topological Semantics for Provability Logics
Thomas Icard, Herbert Simon Postdoctoral Fellow, Carnegie Mellon University, Department of Philosophy, Stanford Univesity.

Click for abstract

This will be a survey of ideas and results on topological interpretations of provability logics, especially polymodal provability logics. Esakia first proved completeness for the basic Gödel-Löb logic of provability with respect to scattered spaces. Abashidze and Blass (independently) proved completeness w.r.t. a particular scattered space defined on the ordinal omega^omega. I will discuss work of my own that extended the Abashidze-Blass result to a fragment of polymodal Gödel-Löb logic, which is complete with respect to a polytopological space on epsilon_0. I will then discuss more recent developments, including joint work with Bezhanishvili and Beklemishev, and work by Fernandez and Joosten, and by Beklemishev and Gabelaia, generalizing much of this.

Recent Events


Workshop: Case Studies of Causal Discovery with Model Search

October 25-27, 2013

Brain scan and causal chart

General Information

The Case Studies of Causal Discovery with Model Search Workshop is focused on applications of causal model search to science. It will include sessions on model search in Genetics, Biology, fMRI, Educational Research, Economics, and other disciplines.

Dates: October 25-27, 2013 (Friday-Sunday)
Location: Carnegie Mellon University, Pittsburgh, PA
The Friday sessions will take place in Rangos Hall (2nd floor, University Center)
The Saturday and Sunday sessions will take place in Baker Hall A53

Workshop Topic:
Computer scientists, statisticians, and philosophers have created a precise mathematical framework for representing causal systems called "Graphical Causal Models." This framework has supported the rigorous description of causal model spaces and the notion of empirical indistinguishability/equivalence within such spaces, which has in turn enabled computer scientists to develop asymptotically reliable model search algorithms for efficiently searching these spaces. The conditions under which these methods are practically useful in applied science is the topic of this workshop. The workshop will bring together scholars from genetics, biology, economics, fMRI-based cognitive neuroscience, climate research, education research, and several other disciplines, all of whom have successfully applied computerized search for causal models toward a scientifically challenging problem. The goals for the workshop are to: (1) to identify strategies for applying causal model search to diverse domain-specific scientific questions; (2) to identify and discuss methodological challenges that arise when applying causal model search to real-world scientific problems; and (3) to take concrete steps toward creating an interdisciplinary community of researchers interested in applied causal model search. We welcome junior scholars and graduate students, and we will host a free introductory tutorial on model search the first morning of the workshop.

Confirmed Speakers:

David Bessler (Economics, Texas A&M)
Frederick Eberhardt (Philosophy, Cal Tech)
Imme Ebert-Uphoff (Electrical & Computer Engineering, Colorado State University)
Kathleen Gates (Quantitative Psychology, University of North Carolina)
Clark Glymour (Philosophy, CMU)
Isabelle Guyon (Clopinet, Berkeley, CA)
Catherine Hanson (Psychology, Rutgers University)
Kevin Hoover (Economics and Philosophy, Duke University)
Marloes Maathuis (Statistics, ETH Zurich)
Alessio Moneta (Economics, Scuola Superiore Sant'Anna)
Sergey Plis (Mind Research Network and University of New Mexico)
Joseph Ramsey (Philosophy, CMU)
Martina Rau (Learning Sciences, Univ. of Wisconsin, Madison)
Richard Scheines (Philosophy, CMU)
Cosma Shalizi (Statistics, CMU)
Bill Shipley (Biology, Sherbrooke University)
Alexander Statnikov (Health Informatics and Bioinformatics, New York University)
Ioannis Tsamardinos (Computer Science, University of Crete)

Workshop web site

Workshop on the Logic of Simplicity

June 7-9 2013

CFE/Studia Logica

Rationale: Ockham's razor is the characteristic bias toward simple hypotheses that has characterized scientific inquiry since Copernicus.  But what is it, exactly?  This workshop aims to revisit that question from a fresh logical perspective.  Potential candidates for the simplicity order include dimensionality, Kolmogorov complexity, and VC dimension.  Candidates for Ockham's razor, itself, include logical theories for revising belief in light of such an order in the deterministic case and a host of model selection methods on the side of statistics and machine learning.   This interdisciplinary workshop will begin to explore a number of new and interesting logical questions at the interface of logic and scientific method.  Which orders are simplicity orders?   Is simplicity relative to questions or subject to other framing effects?  How should a simplicity order be modified in light of new information?  What may one believe in light of a simplicity order and given information?  What should one do if the simplicity order branches?   Are the essential features of a simplicity order preserved by the associated belief revision rule?  Are standard belief revision principles descriptively plausible in scientific applications?  Is simplicity absolute or relative to framing effects?  Is there any normative reason to revise according to simplicity rather than some other principle?  Addressing these fundamental questions promises both to sharpen our conception of scientific method and to broaden our ideas about the logic of belief revision.


Jacek Malinowski, (Editor in Chief of Studia Logica)

Opening remarks

Peter Spirtes (Carnegie Mellon University, CMU).

Searching for Causal Graphs

Oliver Schulte (Simon Fraser University Computer Science).

Topological Simplicity and Inductive Inference

Eric Martin (University of New South Wales Computer Science).

The Four Notions of Complexity of Parametric Logic

Kevin T. Kelly and Hanti Lin (Carnegie Mellon University, Philosophy).

Empirical Simplicity, Efficient Inquiry, and Ockham's Razor

James Delgrande (Simon Fraser University Computer Science).

Believing the Simplest Course of Events

Sven Ove Hannson (University of Stockholm, Philosophy).

Belief change for finite minds

Sonja Smets (ILLC Amsterdam)

Epistemic Topology: problem-solving, belief-revision and simplicity-based priors

Alexandru Baltag (ILLC Amsterdam)

Conditioning as a Universal Learning Method: qualitative, probabilistic and computable updates

Nina Gierasimczuk(ILLC Amsterdam).

Computability and Ockham's Razor 

Vist the Logic of Simplicity web site.

2nd Conference on Games, Interactive Rationality, and Learning (GIRL)

April 23-26, 2013

Lund, Sweden

Cosponsored by the CFE

Vist the GIRL web site

Workshop on Cognition and Formal Theories of Reasoning

March 30, 2013


Niki Pfeifer (LMU & CFE Visiting Fellow)

How People (Ought to) Reason under Uncertainty

Hanti Lin and Kevin T. Kelly (CMU Philosophy)

Propositional Beliefs that Aptly Represent Subjective Probabilities in Light of New Information

Wilfried Sieg (CMU Philosophy)

Structural Proof Theory: Uncovering Capacities of the Mathematical Mind?

Chris Lucas (CMU Psychology)

Bayes net Models of Counterfactual Reasoning

Charles Kemp and Chris Carroll (CMU Psychology)

Hypothesis Space Checking in Everyday Reasoning

David Danks (CMU Philosophy)

Discussion: Logic, Psychology, and Reasoning"

Formal Theories of Reasoning web site.

"Evolution, Learning, and Games".

October 6, 2012


  • 12:00 Lunch
  • 2:00 Rory Smead (Northeastern University)
  • Two Evolutionary Models of Unconditional Spite
  • [MP4]
  • 3:30 Russell Golman (Carnegie Mellon University)
  • Basis of Attraction and Equilibrium Selection with Population Learning Dynamics
  • [MP4]
  • 5:00 Final Thoughts

Tribute to Horacio Arlo-Costa

August 2-4,

Sociedad Argentina De Analisis Filisofico, (SADAF), Buenos Aires.


  • Lavinia Picollo (Universidad de Buenos Aires - CONICET - GAF)
  • Dustin Tucker (Texas Tech University)
  • Vit Puncochar (Faculty of Arts, Charles University in Prague)
  • Diego Tajer (Universidad de Buenos Aires – CONICET)
  • John Collins (Columbia University):
  • Javier Legris and Silvia Lerner (Universidad de Buenos Aires)
  • Claudio Alessio (Universidad Católica de Cuyo)
  • Paul Pedersen (Carnegie Mellon University)
  • Lucas Rosenblatt (Universidad de Buenos Aires – CONICET – GAF)
  • Gustavo Bodanza (Universidad Nacional del Sur)
  • Verónica Becher (Universidad de Buenos Aires)
  • Marcelo Auday and Rodrigo Moro (Universidad Nacional del Sur –
  • David Etlin (University of Groningen)
  • Kevin Kelly (Carnegie Mellon University)

Workshop web site

Workshop on the Foundations of Ockham's Razor

June 22-24, 2012,



Scientific theory choice is guided by judgments of simplicity, a bias frequently referred to as "Ockham's Razor". But what is simplicity and how, if at all, does it help science find the truth? Should we view simple theories as means for obtaining accurate predictions, as classical statistics and machine learning urge? Or should we believe the theories themselves, as Bayesian methods seem to justify? The aim of this workshop is to re-examine the foundations of Ockham's razor, with a firm focus on the connections, if any, between simplicity and truth.


Streaming videos and slides available at the workshop web site

The CFE co-sponsored the First CSLI Workshop on Logic, Rationality and Interaction.

June 1-3, 2012, Cordura Hall, CSLI, Stanford Universtiy


Johan van Benthem, Peter Hawke, Wes Holliday, Tomohiro Hoshi, Thomas Icard, Shane Steinert-Threlkeld.


Workshop web page

The CFE co-sponsored the GIRL (Games, Interactive Rationality, and Learning) conference at the University of Lund, Sweden, on April 19-21, 2012, organized by Emmanuel Genot, Justine Jacot, and Philip Paernamets.

Workshop web page.

Horacio Arlo-Costa

Commemorative Collection for Horacio Arlo-Costa. To honor Horacio Arlo-Costa's memory and influence on all of us in the community, Jeffrey Helzner, Vincent F. Hendricks, Paul Pedersen and Gregory Wheeler will be editing a book with essays on his philosophy, his intellectual biography, his official obituary, words of remembrance from his friends and colleagues, his unpublished manuscripts and notes, and other relevant communications from or about Horacio. If you have words of remembrance, please feel welcome to post them at Choice and Inference under the entry In Memory of Horacio Arlo-Costa, as we will, with your permission, use your words of remembrance for the volume. Please send all other material (correspondences, notes, etc.) to any one of the editors:

In Memoriam: Horacio Arlo-Costa (1956-2011). We deeply regret the sudden passing of CFE Associate Director Horacio Arlo-Costa. The Center's ambitious schedule of six events in its first year of operation was due in large part to Horacio's indefatigable dedication. His stature in formal epistemology is familiar. His tireless enthusiasm, his widespread connections in the field and his renowned, encyclopedic knowledge of the literature and the contributions of others made him an indespensable partner in the wild adventure that constituted the Center's crucial first year of operation. He will be missed sorely. In spite of his many other duties and concerns, Horacio reveled in the CFE's rapid expansion . To vindicate his commitment, the CFE will redouble its efforts to facilitate the cause of formal philosophy in the coming years.

Horacio's obituary

Horacio's funeral arrangements

Horacio's CFE legacy

The Commemorative Colloquium for CFE Associate Director Horacio Arlo-Costa was held on November 19-20, 2011. Thanks to all the speakers for making the Colloquium a great success! Here is the schedule of talks.

The CFE workshop In Search of Answers: The Guiding Role of Questions in Discourse and Epistemology was held on Nov 5, 2011 in 4625 Wean Hall

Schedule and abstracts.


Jeroen Groenendijk, University of Amsterdam
Craige Roberts, Ohio State University
Mandy Simons, Carnegie Mellon University
Hanti Lin, Carnegie Mellon University
Kevin T. Kelly, Carnegie Mellon University

The Episteme annual conference on Social Epistemology was held at the CFE on June 24-26, 2011 in coordination with Alvin Goldmanand Christian List.  Here is the revised schedule and a link to arrangements.

There was a joint CSLI-CFE-San Francisco State workshop on Logic and Formal Epistemology at CSLI, Stanford on May 14 and 15, 2011, organized by Johan van Benthem, Bas van Fraassen, and Kevin van Kelly.  The topics will be learning in epistemic logic and a re-examination of norms in empirical reasoning. Local organizers Peter Hawke, Wes Holliday, Tomohiro Hoshi, and Thomas Icard at Stanford did a fantastic job and the workshop was supported mainly by the generosity of Patrick Suppes and the Department of Philosophy at Stanford. We hope this is the beginning of a long tradition.

On March 16, 12:00-4:00 there was a symposium on uncertain acceptance involving Hannes Leitgeb, Horacio Arlo-Costa, Kevin Kelly, Paul Pedersen, and Hanti Lin in DH.  The symposium compared notes on three new but distinct approaches to the subject. 

The CFE Colloquium series for Spring 2011 was rich, varied, and exciting.  Speakers included Cosma Shalizi, Michiel van Lambalgen, Hannes Leitgeb, Anil Gupta, and Mic Detlefsen.

The workshop on Experience, Heuristics, and Choice: Prospects for Bounded Rationality on Dec 1, 2010 was a great success.  Thanks to all who participated.

The 2010 Nagel Lectures were delivered by Brian Skyrms on Oct. 19-21, 2010.

The CFE Opening Celebration Conference was held on June 26-27, 2010.  Thanks to all who contributed to make it such a huge success!

The CFE Masthead illustrates Doherty Hall,where the new CFE office wing is located  (the windows on the top floor).  Like most of the Carnegie Mellon Campus, Doherty hall was designed in the Beaux-arts style by American architect Henry Hornbostel (1867-1961).  The band across  the bottom of the masthead is taken from the terra-cotta thistle frieze, designed to commemorate Andrew Carnegie, that runs right below the windows of the CFE offices.

Center Overview

In October 2009, the Center for Formal Epistemology was founded to promote research and educational exchanges in Formal Epistemology worldwide. The Center adopts a broad perspective on Formal Epistemology, including philosophically and formally informed, interdisciplinary work in the following areas:

  • bayesian epistemology,
  • belief revision,
  • causation,
  • decision and game theory,
  • philosophical logic (conditional, epistemic, erotetic, dynamic, etc.),
  • formal learning theory,
  • formal approaches in cognitive science,
  • formal theories in the philosophy of science,
  • history of formal epistemology,
  • implicature and pragmatics,
  • philosophy of mathematics,
  • philosophy of statistics,
  • social epistemology.

  • Center activities include:

  • a Visiting Fellows program,
  • a graduate exchange program,
  • a Summer School in Logic and Formal Epistemology for prospective graduate students,
  • an annual, Focused Workshop in Formal Epistemology that rotates in topic,
  • an annual Colloquium Series in Formal Epistemology.