MCMP – Logic

Steve Awodey (Carnegie-Mellon) gives a talk at the MCMP workshop "Carnap on Logic" (3-6 July, 2013) titled "On the Invariance of Logical Truth".

Patricia Blanchette (Notre Dame) gives a talk at the MCMP workshop "Carnap on Logic" (3-6 July, 2013) titled "Applications and Content: Frege and Gödel on Mathematics as Syntax".

Michael Friedman (Stanford) gives a talk at the MCMP workshop "Carnap on Logic" (3-6 July, 2013) titled "From Intuition to Tolerance in Carnap's Philosophy of Mathematics". Abstract: I plan to discuss the evolution of Carnap's views on arithmetic and geometry from Der Raum, through the Aufbau period, to Logical Syntax and the semantic period. I will concentrate on the way in which he consistently distinguished the two cases -- where geometry, in Der Raum, is explicitly tied to spatial intuition, and then, even though it remains distinguished from arithmetic, its ties to spatial intui- tion become empirical rather than a priori. The character of Carnap's generally tolerant attitude towards philosophical disputes in the foundations of mathematics thereby changes as well. Carnap's attitude towards intuition in the arithmetical case, finally, becomes clarified in his exchange with E. W. Beth in the Schilpp volume -- and this clarifies his application of the principle of tolerance in this case as well.

Michael Dunn (Bloomington) gives a talk at the MCMP Colloquium (25 June, 2013) titled "Arrows, Relevance, and Relations*". Abstract: The van Benthem-Venema "arrow logics" are abstractly well-motivated and have epistemic applications, e.g., to the logic of information flow and information update. I explore the relationships between the van Benthem-Venema semantics for arrow logics and the Routley-Meyer semantics for relevance logics, and show that there is a translation between the two. I will also briefly discuss the relationship to Barwise’s (1993) logic of "channels." I compare van Benthem’s version of the semantics for arrow logic aimed at relation algebras with my own generalization of the Routley-Meyer semantics aimed at the same target. I use my (1993, 2001) representation of relation algebras based on Routley-Meyer frames to give an equivalent representation of relation algebras based on frames for arrow logic. A philosophical interpretation is given to this representation as showing that each element of a relation algebra can be interpreted as a set of relations (not as a single relation –Lyndon showed this is impossible). This interpretation is thus a type level higher than the natural interpretation of an element as just a relation, and can be viewed in terms of interpreting each element as a relational database. The operations of a relation algebra can then be interpreted as operations combining relational databases.

Jakub Szymanik (Amsterdam) gives a talk at the MCMP Colloquium (12 June, 2013) titled "From Logic to Behavior". Abstract: In this talk I will explore the applicability of modern logic and computation theory in cognitive science. I will show how logic can be used to build cognitive models in order to explain and predict human behavior. I will also illustrate the use of logical and computational toolboxes to evaluate (not necessarily logical) cognitive models along the following dimensions: (i) logical relationships, such as essential incompatibility or essential identity; (ii) explanatory power; (iii) computational plausibility. I will argue that logic is a general tool suited for cognitive modeling, and its role in psychology need not be restricted to the psychology of reasoning. Taking Marr's distinctions seriously I will also discuss how logical studies can improve our understanding of cognition by proposing new methodological perspectives in psychology. I will illustrate my general claims with examples of the successful research on the intersection of logic and cognitive science. I will mostly talk about two research projects I have been recently involved in: computational semantics for generalized quantifiers in natural language and logical models for higher order social cognition. The major focus will be computational complexity and its interplay with "difficulty" as experienced by subjects in cognitive science.

Martin Fischer (MCMP/LMU) gives a talk at the MCMP workshop "Truth and Paradox" (24-25 May, 2013) titled "Truth and Speed-up".

Lionel Shapiro (Connecticut) gives a talk at the MCMP workshop "Truth and Paradox" (24-25 May, 2013) titled "Naive Sequent Structure, Contraction and Paradox".

David Ripley (Melbourne) gives a talk at the MCMP workshop "Truth and Paradox" (24-25 May, 2013) titled "Contractions of noncontractive consequence".

Johannes Stern (MCMP/LMU) gives a talk at the MCMP workshop "Truth and Paradox" (24-25 May, 2013) titled "Necessities and Necessary Truths. A Proof-Theoretic Addendum".

Chris Fermüller (Vienna) gives a talk at the MCMP Colloquium (2 May, 2013) titled "Semantic games and hypersequents: a case study in many valued reasoning". Abstract: For a quite a while it had been an open problem whether there is an analytic (cut-free) calculus for infinite valued Lukasiewicz logic, one of threefundamental many valued logics that lie at the centre of interest in contemporary mathematical fuzzy logic. The hypersequent calculus HL presented by Metcalfe, Gabbay, and Olivetti in 2004/5 settled the question positively; but HL did not fit well into the family of sequent and hypersequent systems for related nonclassical logics. In particular it remained unclear in what sense HL provides an analysis of logical reasoning in a many valued context. On the other hand, already in the 1970s Robin Giles had shown that a straightforward dialogue game, combined with a specific way to calculate expected losses associated with bets on the results on `dispersive experiments' leads to a characterisation of Lukasiewizc logic. We illustrate how these seemingly unrelated results fit together: the logical rules of HL naturally emerge from a systematic search for winning strategies in Giles's game. This amounts to a rather tangible interpretation of hypersequents that can be extended to other logics as well.