The work concerns automatic generation of logical specifications from requirements models. Logical specifications obtained in such a way can be subjected to formal verification using deductive reasoning. Formal verification concerns correctness of a model behaviour. Reliability of the requirements engineering is essential for all phases of software development processes. Deductive reasoning is ...

In this paper we discuss Gabbay’s idea of basing nonmonotonic deduction on semantic consequence in intuitionistic logic extended by a consistency operator and Turner’s suggestion of replacing the intuitionistic base system by Kleene’s three-valued logic. It is shown that a certain counterintuitive feature of these approaches can be avoided by using Nelson’s constructive logic N instead of intui...

1 Introduction In this paper we provide very broad notions of deduction and consequence for logic programs (so-called LP-deduction relations and LP-consequence relations), and we prove that under very modest assumptions, an LP-deduction relation will be either unsound or incomplete with respect to every LP-consequence relation. Throughout this paper we assume a non-logical alphabet, K, which in...

The paper discusses work in progress on developing a tabular deduction method for multimodal logical grammar. The method is based on a compilation procedure, a single elimination rule for multiplicative and additive (t) binary operators, and two rules defining residuation for the unary modals i/ #i . The method aims to achieve for multimodal logical grammar what chart-based parsing does for CFG...

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...