The ad hominem argument of Berkeley’s Analyst

This paper responds to two issues in interpreting George Berkeley’s Analyst. First, it explains why the text contains no discussion of religious mysteries or points of faith, despite the claims of the text's subtitle; I argue that the subtitle must be understood, and its success assessed, in conjunction with material external to the text. Second, it’s unclear how naturally the arguments of the Analyst sit with Berkeley’s broader views. He criticizes the methodology of calculus and conceptually problematic entities, and the extent to which they require one to bend the rules of classical mathematics. Yet, elsewhere, Berkeley’s opinion of classical mathematics and its intelligibility is low, and he defends a pragmatic approach to word meaning that should not find fault with so functionally successful a theory. The ad hominem intention of the text makes it difficult to discern to what extent Berkeley is committed to the sincerity of these criticisms. This component of the text is rarely discussed, but I argue that when trying to decide what Berkeley’s true position is in the Analyst, we should treat its ad hominem component as its primary intention.     

Sequent Calculi and Decision Procedures for Weak Modal Systems

We investigate sequent calculi for the weak modal (propositional) system reduced to the equivalence rule and extensions of it up to the full Kripke system containing monotonicity, conjunction and necessitation rules. The calculi have cut elimination and we concentrate on the inversion of rules to give in each case an effective procedure which for every sequent either furnishes a proof or a finite countermodel of it. Applications to the cardinality of countermodels, the inversion of rules and the derivability of Löb rules are given.     

On the matrix formulation of Kaiser's varimax criterion

The author provides a full-fledged matrix derivation of Sherin's matrix formulation of Kaiser's varimax criterion. He uses matrix differential calculus in conjunction with the Hadamard (or Schur) matrix product. Two results on Hadamard products are presented.     

Distributive Full Lambek Calculus Has the Finite Model Property

We prove the Finite Model Property (FMP) for Distributive Full Lambek Calculus (DFL) whose algebraic semantics is the class of distributive residuated lattices (DRL). The problem was left open in [8, 5]. We use the method of nuclei and quasi–embedding in the style of [10, 1]. Presented by Daniele Mundici.     

Correspondence Results for Relational Proof Systems with Application to the Lambek Calculus

We present a general framework for proof systems for relational theories. We discuss principles of the construction of deduction rules and correspondences reflecting relationships between semantics of relational logics and the rules of the respective proof systems. We illustrate the methods developed in the paper with examples relevant for the Lambek calculus and some of its extensions.     

Proof Nets for the Multimodal Lambek Calculus

We present a novel way of using proof nets for the multimodal Lambek calculus, which provides a general treatment of both the unary and binary connectives. We also introduce a correctness criterion which is valid for a large class of structural rules and prove basic soundness, completeness and cut elimination results. Finally, we will present a correctness criterion for the original Lambek calculus Las an instance of our general correctness criterion.     

Game Semantics for the Lambek-Calculus: Capturing Directionality and the Absence of Structural Rules

In this paper, we propose a game semantics for the (associative) Lambek calculus. Compared to the implicational fragment of intuitionistic propositional calculus, the semantics deals with two features of the logic: absence of structural rules, as well as directionality of implication. We investigate the impact of these variations of the logic on its game semantics. Presented by Wojciech Buszkowski     

Predication and cognitive context: Between minimalism and contextualism

In this paper, we suggest a strategy for modelling cognitive context within a truth‐conditional semantics, using Asher's model of predication. This allows us to introduce the notion of type presupposition intended as a lexical constraint to the composition of the truth‐conditional content. More specifically, we suggest that this model of predication produces a notion of truth‐conditional meaning where the cognitive context fixes a set of lexical restrictions and forced modifications. We conclude that this model might offer an intermediate position between Minimalism and Contextualism: an account that provides intuitive truth conditions within a formal semantic theory.