June 7-9 2013
Location: Adamson Wing, Baker Hall, CMU Campus
All are invited to attend. CMU Summer School attendees are welcome.
Jointly sponsored by Studia Logica and the John Templeton Foundation.
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.
Schedule:
Friday, June 7, 2013:
9:00-9:30 Jacek Malinowski, (Editor in Chief of Studia Logica)
Opening remarks
9:30-10:45 Peter Spirtes (Carnegie Mellon University, CMU).
Searching for Causal Graphs
11:00-12:15 Oliver Schulte (Simon Fraser University Computer Science).
Topological Simplicity and Inductive Inference
12:15-2:30 Lunch.
2:30-3:45 Eric Martin (University of New South Wales Computer Science).
The Four Notions of Complexity of Parametric Logic
4:00-5:15 Kevin T. Kelly and Hanti Lin (Carnegie Mellon University, Philosophy).
Empirical Simplicity, Efficient Inquiry, and Ockham's Razor
5:30-6:00 Discussion
6:30 Dinner
Saturday, June 8, 2013:
9:00-10:15 James Delgrande (Simon Fraser University Computer Science).
Believing the Simplest Course of Events
10:30-11:45 Sven Ove Hannson (University of Stockholm, Philosophy).
Belief change for finite minds
12:00-2:00 Lunch.
2:00-3:15 Sonja Smets (ILLC Amsterdam)
Epistemic Topology: problem-solving, belief-revision and simplicity-based priors
3:30-4:45 Alexandru Baltag (ILLC Amsterdam)
Conditioning as a Universal Learning Method: qualitative, probabilistic and computable updates
5:00-6:15 Nina Gierasimczuk(ILLC Amsterdam).
Computability and Ockham's Razor
6:30 Dinner
Sunday, June 9, 2013:
9:30-11:00 Round Table Discusion.
Abstracts:
Friday, June 7, 2013:
9:00-9:30 Jacek Malinowski, (Editor in Chief of Studia Logica)
Opening remarks
9:30-10:45 Peter Spirtes (Carnegie Mellon University, CMU).
Searching for Causal Graphs
Over the last 25 years, a number of algorithms that search for causal models from non-experimental data have been developed. These search algorithms typically represent causal models as directed acylic graphs, and take as a fundamental assumption the Causal Markov Assumption, which states that each variable is independent of its non-effects conditional on its immediate causes. The Causal Markov Assumption associates with each causal graph G a set of probability distributions P(G) compatible with G and imposes a natural simplicity partial order on the causal graphs. In an idealized form these search aglorithms take as input a probability distribution, and output a causal graph or set of causal graphs compatible with the distribution. In this talk I will describe how the simplicity partial order can be used to guide the order in which the search is performed, and different possible responses to cases where there is more than one maximally simple graph G compatible with a given input distribution.
11:00-12:15 Oliver Schulte (Simon Fraser University Computer Science).
Topological Simplicity and Inductive Inference
In this talk I will show how a geometric notion of simplicity from the 19th century can be applied to modern problems of inductive inference, including: 1) Various Goodmanian problems of induction, and 2) Inferring the causal structure of a domain from observed significant correlations (constraint-based Bayes net learning). Cantor proposed a classic measure of the complexity of a set of points in a topological space based on the set's boundary. While the geometry of boundaries may seem far from questions of belief and induction, Kelly has shown that point-set topology becomes a theory of learning when we view a space of possible hypotheses as a topological space. In a learning topology, Cantor's measure assigns a complexity rank to each hypothesis. Using Occam's Razor to minimize topological complexity selects the natural projection rule in Goodmanian Riddles of Induction, and defines a plausible method for learning causal structure.
12:15-2:30 Lunch.
2:30-3:45 Eric Martin (University of New South Wales Computer Science).
The Four Notions of Complexity of Parametric Logic
We present Parametric logic, a logical framework where a generalised notion of logical consequence is defined as a function of a number of parameters (possible worlds, possible axioms, possible data) set to particular values. Depending on the values of the parameters, this generalised notion of logical consequence might or might not be compact. Given an ordinal beta, a notion of beta-compactness is defined, with classical compactness corresponding to the case where beta = 0.. We argue that deduction is captured by 0-compactness and induction by 1-compactness. We show that the notion of beta-compactness is closely related to the notion of learning with fewer than beta mind changes, and also sheds new lights on nonmonotonic reasoning. Classical logic is a particular instance of this framework where the generalised notion of logical consequence is the classical, compact, notion of logical consequence, hence where ``logical consequence'' and ``deductive consequence'' are the same notions. But when the generalised notion of logical consequence is not compact, the beta-consequences of a theory withbeta ranging over the ordinals form a hierarchy which is closely related to a particular topological space and the stratification of its Delta-2 sets by the difference hierarchy. A proof theory is presented which necessitates the introduction of a specific syntactic normal form. Putting everything together, four notions of complexity, model-theoretic (generalised compactness), topological (level of the difference hierarchy), syntactic (kind of normal form) and learning-theoretic (number of mind changes) have strong relationships between each other and characterise forms of logical inference which are more and more uncertain, more and more subjected to potential revisions. In this framework, induction is a particular form of inference alongside deduction, where an inductive consequence can be computed from a set of premises following the application of some rules of inference, similarly to the fact that deductive consequences can be computed from a set of premises following the application of some rules of inference. If the "game of deduction'' is to find interesting deductive consequences, we could question where the "game of induction'' should be any different. A deep result which can be proved deductively can have a simple expression; still what is sought after is usually not simplicity, but how much the result reveals about the structures which are the object of scientific inquiry. It is legitimate to question whether results which can be proved inductively are any different.
4:00-5:15 Kevin T. Kelly and Hanti Lin (Carnegie Mellon University, Philosophy).
Ockham's Razor as Belief Revision With Respect to Empirical Simplicity
We present an axiomatic theory of empirical complexity relative to an empirical problem, which specifies possible information states and possible answers to an empirical question. The theory generalizes topological difference complexity and recovers uniquely the standard, branching search order for causal networks. Next, we define worst-case efficiency of empirical inquiry relative to empirical simplicity in a way that does not beg questions whether the actual world is simple. Ockham's razor is then a belief revision strategy relative to the simpicity order. But which? That depends in an interesting and important way on the strategic losses that are assumed in underlying notion of efficient inquiry, as we will illustrate. A particularly natural version of Ockham's razor corresponds to the aim of minimizing losses in true content en route to convergence to the true answer to the empirical question.
5:30-6:00 Discussion
6:30 Dinner
Saturday, June 8, 2013:
9:00-10:15 James Delgrande (Simon Fraser University Computer Science).
Believing the Simplest Course of Events
This talk describes a theory in which an agent may execute actions and sense
its environment. The agent have incomplete or incorrect beliefs; as well, actions may fail, or have unintended consequences, or may have outcomes that are impossible to predict. The goal is to maintain an agent's belief state wherein the agent's beliefs accord with the simplest, or most plausible, sequence of actions consistent with its prior beliefs and sensing actions. Hence, for example, an agent that senses that a light is on, and again later senses that it is on, will believe that the light has remained on and not that it was toggled some (even) number of times. Similarly, the agent may also subsequently revise its beliefs if it learns that a particular sequence of actions could not have been the case.This account is based on an epistemic extension to the situation calculus, that is, a first-order theory of reasoning about action that accommodates sensing actions. Our position is that nondeterminism is an epistemic phenomenon, and arises from an agent's limited awareness and perception of a deterministic world. The account offers several advantages: an agent has a set of categorical (as opposed to probabilistic) beliefs, yet can deal with equally-likely outcomes (such as in flipping a fair coin) or with outcomes of differing plausibility (such as an action that may on occasion fail). It maintains as its set of contingent beliefs the most plausible, or simplest, picture of the world, consistent with its beliefs and actions it believes it executed; yet it may modify these in light of later information.
10:30-11:45 Sven Ove Hannson (University of Stockholm, Philosophy).
Belief change for finite minds
Standard models of belief change such as partial meet contraction operate by making choices among cognitively inaccessible objects such as possible worlds or maximal consistent subsets that lack a finite representation. Finite belief bases avoid that difficulty, but bring in others. An alternative approach is presented in which changes take place on finitely representable belief sets but no distinction is made between different belief bases for the same belief set. Reference to infinite objects is avoided by changing the level of selection. Choice functions can operate directly on the set of possible outcomes (the credible and reachable finite-based belief sets) rather than on infinite and cognitively inaccessible objects.
12:00-2:00 Lunch.
2:00-3:15 Sonja Smets (ILLC Amsterdam)
Epistemic Topology: problem-solving, belief-revision and simplicity-based priors
3:30-4:45 Alexandru Baltag (ILLC Amsterdam)
Conditioning as a Universal Learning Method: qualitative, probabilistic and computable updates
5:00-6:15 Nina Gierasimczuk (ILLC Amsterdam).
Computability and Ockham's Razor
In this talk I will show how the principle of Ockham's Razor, understood as the requirement of conservativity and efficiency of learning functions, interacts with the uniform decidability of epistemic spaces in the context of computable learners.
6:30 Dinner
Sunday, June 9, 2013:
9:30-11:00 Round Table Discusion.
June 7-9 2013
April 23-26, 2013
Lund, Sweden
Cosponsored by the CFE
March 30, 2013
Location: Wean Hall 4625, Carnegie Mellon University
All are invited to attend
Program:
9:00 Niki Pfeifer (LMU & CFE Visiting Fellow)
How People (Ought to) Reason under Uncertainty
Abstract: Mental probability logic" (MPL) consists of normative and descriptive theory components. The normative one is based on coherence based probability logic. It formulates reasoning problems in terms of arguments consisting of premises and conclusions. The uncertainty of the premises is transmitted deductively to the conclusion. The descriptive component of MPL investigates empirical hypothesis which are made precise by MPL's normative theory component. In my talk I show how the normative and descriptive theory elements of MPL interact. I illustrate my approach with selected formal and empirical work on nonmonotonic reasoning, Aristotle's thesis, and first steps towards a coherence based probability semantics of Aristotelian syllogisms.
10:10 Hanti Lin and Kevin T. Kelly (CMU Philosophy)
Propositional Beliefs that Aptly Represent Subjective Probabilities in Light of New Information
Abstract: If Bayesians are right, one's doxastic state should be modeled by subjective probabilities. But in traditional epistemology, in logic-based artificial intelligence, and in everyday life, one's doxastic state is usually expressed in a qualitative, binary way: either one accepts (believes) a proposition or one does not. What is the relationship between qualitative and probabilistic belief? A standard approach is to identify propositional belief with certainty (Levi 1967, Douven 2002) or near certainty (Kyburg 1961, Foley 1992, Weinstraub 2001). But that is too skeptical---one reasons and plans all the time with propositions that fall short of near-certainty: e.g., that the grocery store will be open after work. We present an alternative viewpoint according to which propositional beliefs should crudely but aptly represent one's probabilistic credences in terms of propositions. Aptness should include responses to new information: if propositional belief state K aptly represents degrees of belief p then the revised belief state K*E should aptly represent the conditional degrees of belief p(.|E). We explain how to characterize synchronic aptness and qualitative belief revision to ensure diachronic aptness in the sense just defined. We also show that diachronic aptness in the sense just described is impossible if acceptance is based on thresholds or if qualitative belief revision is based on the familiar AGM belief revision theory of Alchourron, Gardenfors, and Makinson 1985.
10:20 Wilfried Sieg (CMU Philosophy)
Structural Proof Theory: Uncovering Capacities of the Mathematical Mind?
Abstract: What is it that shapes arguments into mathematical proofs that are intelligible to us, and what is it that allows us (or machines) to find proofs efficiently? – These are the informal questions I intend to address. Two aspects of mathematical experience play a significant role: the abstract ways of the axiomatic method used in modern mathematics and the concrete ways of proof construction suggested by modern proof theory. The subtle interaction between understanding and reasoning, i.e., between introducing concepts and proving theorems, is crucial and suggests principles for structuring proofs conceptually. My partly historical and partly theoretical investigations are complemented by experimentation with a strategically guided proof search algorithm. The issues will be illustrated by considering three theorems and their proofs: the Pythagorean theorem, the Cantor Bernstein theorem, and Goedel's incompleteness theorem.
12:20 Lunch
2:30 Chris Lucas (CMU Psychology)
Bayes net Models of Counterfactual Reasoning
Abstract: Bayesian networks have been used to account for many aspects of causal reasoning, including inferences about counterfactual scenarios. We present a Bayes net model of counterfactual reasoning that generalizes and extends the work of Pearl (2000). The model distinguishes between counterfactual observations and counterfactual interventions, and can reason about both backtracking and non-backtracking counterfactuals. Several experiments demonstrate that our model accounts better for human inferences than Pearl's original proposal and a more recent Bayes net account developed by Rips (2009).
3:40 Charles Kemp and Chris Carroll (CMU Psychology)
Hypothesis Space Checking in Everyday Reasoning
Abstract: The process of discovering a new hypothesis often begins with the recognition that all of the hypotheses currently under consideration are wrong. While this sort of falsification is straightforward when the observations are strictly incompatible with the hypotheses, a more challenging situation arises when the observations are implausible under the hypotheses but not incompatible with them. We propose a formal account, inspired by falsificationism and statistical model checking, as an explanation for how people decide that all of their current hypotheses are probably wrong. In our talk, we will describe a psychology experiment that contrasted this account with Bayesian inference. We conclude that although Bayesian reasoning can explain inference within a given hypothesis space, it cannot explain how people decide that they need to look beyond their current hypothesis space.
4:40 David Danks (CMU Philosophy)
Discussion: Logic, Psychology, and Reasoning"
Abstract: I will synthesize the preceding talks and set the stage for an extended discussion among all participants.
5:50 Program concludes
Visit the Foundations of Ockham's Razor web page.
October 6, 2012, CFE Conference: "Evolution, Learning, and Games".
Location: Wean Hall 4625, Carnegie Mellon University
August 2-4, Tribute to Horacio Arlo-Costa, Sociedad Argentina De Analisis Filisofico, Buenos Aires.
Speakers:
An Interdisciplinary CFE Workshop on the Foundations of Ockham's Razor was held on June 22-24, 2012, Adamson Wing, Baker Hall, Carnegie Mellon University
Rationale:
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.
Speakers:
Streaming videos and slides available at the workshop web page
The CFE co-sponsored the First CSLI Workshop on Logic, Rationality and Interaction.
June 1-3, 2012, Cordura Hall, CSLI, Stanford Universtiy
Organizers:
Johan van Benthem, Peter Hawke, Wes Holliday, Tomohiro Hoshi, Thomas Icard, Shane Steinert-Threlkeld.
Speakers:
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.
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 funeral arrangements
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
Speakers:
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.