There are at least two reasonable types of logical inferentialism. The first type of inferentialism views the meaning of a connective in proof-theoretic terms, having no truck with ordinary model theory except in its role as an instrument to illuminate various proof-theoretic features of a connective. The second type of inferentialist is more modest, allowing that we have some prior conception ...

In this paper, we shortly review two formal approaches in verification of security protocols; model checking and theorem proving. Model checking is based on studying the behavior of protocols via generating all different behaviors of a protocol and checking whether the desired goals are satisfied in all instances or not. We investigate Scyther operational semantics as n example of this...

We used behavioral and functional magnetic resonance imaging (fMRI) methods to probe the cerebral organization of a simple logical deduction process. Subjects were engaged in a motor trial-and-error learning task, in which they had to infer the identity of an unknown 4-key code. The design of the task allowed subjects to base their inferences not only on the feedback they received but also on t...

We show how labelled deductive systems can be combined with a logical framework to provide a natural deduction implementation of a large and well-known class of propositional modal logics (including K, D, T, B, S4, S4:2, KD45, S5). Our approach is modular and based on a separation between a base logic and a labelling algebra, which interact through a xed interface. While the base logic stays xe...

A Rasiowa-Sikorski system is a sequence-type formalization of logics based on building decomposition trees of formulae labelled with sequences of formulae. Proofs are nite decomposition trees with leaves having \fundamental", valid labels. The system is dual to the tableau system. The author gives examples of applying the R-S formalism to various C.S and A.I. logic, including a logic for reason...

We define the notions of a canonical inference rule and a canonical constructive system in the framework of strict single-conclusion Gentzen-type systems (or, equivalently, natural deduction systems), and develop a corresponding general non-deterministic Kripke-style semantics. We show that every strict constructive canonical system induces a class of non-deterministic Kripke-style frames, for ...

We give a direct, purely arithmetical and elementary proof of the strong normalization of the cut-elimination procedure for full (i.e. in presence of all the usual connectives) classical natural deduction.

It is shown the complete equivalence between the theory of continuous (enumeration) fuzzy closure operators and the theory of (effective) fuzzy deduction systems in Hilbert style. Moreover, it is proven that any truth-functional semantics whose connectives are interpreted in [0,1] by continuous functions is axiomatizable by a fuzzy deduction system (but not by an effective fuzzy deduction syste...

The combinatorics of proof-search in classical propositional logic lies at the heart of most eecient proof procedures because the logic admits least-commitment search. The key to extending such methods to quantiiers and non-classical connectives is the problem of recovering this least-commitment principle in the context of the non-classical/non-propositional logic; i.e., characterizing when a l...