ix I Categorial Type Logics 1 1 The Logical Approach in Linguistics 3 1.1 Rule-Based Categorial Grammars . . . . . . . . . . . . . . . . . . . . . . 3 1.1.1 Classical Categorial Grammar . . . . . . . . . . . . . . . . . . . . 4 1.1.2 Combinatory Categorial Grammar . . . . . . . . . . . . . . . . . 6 1.2 A Logic of Types: Lambek 1958 . . . . . . . . . . . . . . . . . . . . . . . 8 1.2.1 Parsing ...

While inductive and deductive reasoning are considered distinct logical and psychological processes, little is known about their respective neural basis. To address this issue we scanned 16 subjects with fMRI, using an event-related design, while they engaged in inductive and deductive reasoning tasks. Both types of reasoning were characterized by activation of left lateral prefrontal and bilat...

During the last decade computational models of argument have emerged as a successful approach to the formalization of commonsense reasoning, encompassing many other alternative formalisms. Common elements can be identified in such frameworks along with a number of particular features which make it difficult to compare them with each other from a logical viewpoint. This paper presents a unifying...

Dedukti has been proposed as a universal proof checker. It is a logical framework based on the λΠcalculus modulo that is used as a backend to verify proofs coming from theorem provers, especially those implementing some form of rewriting. We present a shallow embedding into Dedukti of proofs produced by Zenon Modulo, an extension of the tableau-based first-order theorem prover Zenon to deductio...

b b b b b b b b b b b b b b b b b b b Abstract The central problem in automated deduction is the explosive growth of search spaces when proof length increases. In this paper, a con-nectionist approach for learning search-control heuristics for automated deduction systems is presented. In particular, we show how folding architecture networks, a new type of neural networks capable of solving supe...

The well-known embedding of intuitionistic logic into classical modal logic means that intuitionistic logic can be viewed as a calculus of labelled deduction on multiple-conclusion sequents, where the labels are the Kripke worlds of the modal embedding. The corresponding natural deduction system constitutes a type system for programs using control operators such as letcc that capture the curren...

Deduction Modulo implements Poincaré’s principle by identifying deduction and computation as different paradigms and making their interaction possible. This leads to logical systems like the sequent calculus or natural deduction modulo. Even if deduction modulo has been shown to be logically equivalent to first-order logic, proofs in such systems are quite different and dramatically simpler wit...

In this paper, we consider multiplicative linear logic (MLL) from an automated deduction point of view. Linear logic is more expressive than classical and intuitionistic logic and has an undirectional character due to the particular treatment of negation and the absence of structural rules. Considering this new logical framework to make logic programming or programming with proofs (extracting p...