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In this article we introduce the Logic and Law corner of this journal. We will discuss a number of ways in which logic has been used in AI and Law, and give some of the key references to previous work on these topics. We will also list some important questions which we see as ready for further...
In an earlier work (Abdulla et al. (2000, Information and Computation, 160, 109–127)) we presented a general framework for verification of infinite-state transition systems, where the transition relation is monotonic with respect to a well quasi-ordering on the set of states. In this article,...
When a physicist performs a quantic measurement, new information about the system at hand is gathered. This article studies the logical properties of how this new information is combined with previous information. It presents Quantum Logic as a propositional logic under two connectives: negation...
This article presents an algorithm that, besides calculating the number of models of a propositional logic theory, also determines the distribution of these models among the terms of a disjunctive normal form representation of the theory. Using prime implicants to represent the target theory, in...
Fibring is a metalogical constructor that permits to combine different logics by operating on their deductive systems under certain natural restrictions, as for example that the two given logics are presented by deductive systems of the same type. Under such circumstances, fibring will produce a...
In this article we give a cut elimination procedure for two-sided sequent system of classical Lambek logic and, on the basis of the presented procedure, a new proof of decidability for this logic.
For two propositional fuzzy logics, we present analytic proof calculi, based on relational hypersequents. The logic considered first, called MŁ , is based on the finite ordinal sums of Łukasiewicz t-norms. In addition to the usual connectives—the conjunction ⊙, the implication → and the...
Vector logic is a matrix–vector representation of the logical calculus inspired in neural network models. In this algebraic formalism, the truth values map on orthonormal Q -dimensional vectors, the monadic operations are represented by square matrices, and the dyadic operations produce...
Verification problems require to reason in theories of data structures and fragments of arithmetic. Thus, decision procedures for such theories are needed, to be embedded in, or interfaced with, proof assistants or software model checkers. Such decision procedures ought to be sound and complete,...
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