Pacuit: Dynamic Logics of Evidence Based Beliefs

Dynamic Logics of Evidence Based Beliefs
Eric Pacuit (University of Maryland)
4:15 PM, Friday, November 1, 2013
Room 4419, CUNY GC

Abstract. The intuitive notion of evidence has both semantic and syntactic features. In this talk, I introduce and motivate an evidence logic for an  agents faced with possibly contradictory evidence from different sources. The logic is based on a neighborhood semantics, where a neighborhood N indicates that the agent has reason to believe that the true state of the world lies in N. Further notions of relative plausibility between worlds and beliefs based on the ordering are then defined in terms of this evidence structure. The semantics invites a number of natural special cases, depending on how uniform we make the  evidence sets, and how coherent their total structure. I will give an overview of the main axiomatizations for different classes of models and discuss logics that describe the dynamics of changing evidence, and the resulting language extensions. I will also discuss some intriguing connections  with logics of belief revision.

This is joint work with Johan van Benthem and David Fernandez-Duque.

Rad: Learning Conditionals

Learning Conditionals
Soroush Rafiee Rad (Tilburg University)
Thursday, July 18, 4:15 PM
Room 4421, CUNY GC
Abstract. Modeling how to learn an indicative conditional has been a major challenge for Formal Epistemologists. One proposal to meet this challenge is to request that the posterior probability distribution minimizes the Kullback-Leibler divergence to the prior probability distribution, taking the learned information as a constraint (expressed as a conditional probability statement) into account. This proposal has been criticized in the literature based on several clever examples. In this paper, we revisit four of these examples and show that one obtains intuitively correct results for the posterior probability distribution if the underlying probabilistic models reflect the causal structure of the scenarios in question.

Dogramaci: The Varieties of Validity Worth Wanting

The Varieties of Validity Worth Wanting
Sinan Dogramaci  (Texas)
Thursday, April 11th, 4:10 PM
716 Philosophy Hall, Columbia University

Abstract. I ask whether the validity of a Modus Ponens inference is any part of the explanation of why the inference is, in any sense, a good or valuable inference. I argue for the following. On the orthodox understanding of validity, a semantic understanding, validity has no explanatory relevance to the reasoning’s value. On a metaphysical understanding of validity, one definable in terms of possible worlds, validity is relevant to a partial, but crucially incomplete, explanation of the reasoning’s value. The complete explanation of the reasoning’s value must also appeal to a substitutional understanding of validity, a notion once advocated by Quine.

Halpern: Constructive Decision Theory

Constructive decision theory: Decision theory with subjective states and outcomes
Joe Halpern (Cornell)
February 15, 2013, 4 PM,
CUNY Mathematics Lounge, 4th floor
Abstract. The standard approach in decision theory (going back to Savage) is to place a preference order on acts, where an act is a function from states to outcomes. If the preference order satisfies appropriate postulates, then the decision maker can be viewed as acting as if he has a probability on states and a utility function on outcomes, and is maximizing expected utility. This framework implicitly assumes that the decision maker knows what the states and outcomes are. That isn’t reasonable in a complex situation. For example, in trying to decide whether or not to attack Iraq, what are the states and what are the outcomes? We redo Savage viewing acts essentially as syntactic programs. We don’t need to assume either states or outcomes. However, among other things, we can get representation theorems in the spirit of Savage’s theorems; for Savage, the agent’s probability and utility are subjective; for us, in addition to the probability and utility being subjective, so is the state space and the outcome space. I discuss the benefits, both conceptual and pragmatic, of this approach. As I show, among other things, it provides an elegant solution to framing problems.

This is joint work with Larry Blume and David Easley. No prior knowledge of Savage’s work is assumed.