Deduction modulo and Supernatural deduction are two extentions of predicate logic with computation rules. Whereas the application of computation rules in deduction modulo is transparent, these rules are used to build non-logical deduction rules in Supernatural deduction. In both cases, adding computation rules may jeopardize proof normalization, but various conditions have been given in both ca...

Cooper’s storage technique for scoping in situ operators has been employed in theoretical and computational grammars of natural language (NL) for over thirty years, but has been widely viewed as ad hoc and unprincipled. Recent work by Pollard within the framework of convergent grammar (CVG) took a step in the direction of clarifying the logical status of Cooper storage by encoding its rules wit...

Live Logic is an integrated approach for support of the learning and decision making in conditions of uncertainty. The approach covers both induction of probabilistic logical hypotheses from known examples and deduction of the plausible solution for an unknown case based on the inducted hypotheses. The induction method generalizes empirical data, discovering statistical patterns, expressed in l...

We prove in HOL that three proof systems for classical rst-order predicate logic, the Hilbertian axiomatization, the system of natural deduction, and a variant of sequent calculus, are isomorphic. The isomorphism is in the sense that provability of a conclusion from hypotheses in one of these proof systems is equivalent to provability of this conclusion from the same hypotheses in the others. P...

The worst-case complexity of cut elimination in sequent calculi for first order based logics is investigated in terms of the increase in logical depth of the deduction. It is shown that given a calculus satisfying a general collection of sufficient conditions for cut elimination and given a deduction with cuts, there exists a cut free deduction with a logical depth, in the worst case, hyper-exp...

We present and discuss various formalizations of Modal Logics in Logical Frameworks based on Type Theories. We consider both Hilbertand Natural Deduction-style proof systems for representing both truth (local) and validity (global) consequence relations for various Modal Logics. We introduce several techniques for encoding the structural peculiarities of necessitation rules, in the typed λ-calc...

This chapter aims to introduce the reader to the basic issues surrounding the design and implementation of intelligent agents. It begins by motivating the idea of an agent, presents a definition of agents and intelligent agents. The article then goes on to discuss four major approaches to building agents. First, logic based architectures are reviewed, in which decision-making is viewed as logic...

We present a method for defining logical frameworks as a collection of features which are defined and behave independently of one another. Each feature is a set of grammar clauses and rules of deduction such that the result of adding the feature to a framework is a conservative extension of the framework itself. We show how several existing logical frameworks can be so built, and how several mu...