On resolution strategies with weak factorization

Linear-type resolution strategies using a simplified modification of the factorization rule for ordered clause are investigated in the paper. The proofs of their soundness and completeness are based on a so-called literal calculus. Peculiarities of inference search with the help of such strategies are demonstrated by means of examples.В роботі досліджуються резолюційні стратегії лінійного типу для впорядкованих диз'юнктів, що використовують ослаблений варіант правила факторізациі. Доведення їхньої коректності та повноти спирається на так зване літеральне числення. Особливості виведення за допомогою таких стратегій демонструються на прикладах

Monotone Logic Programming

We propose a notion of an abstract logic. Based on this notion, we define abstract logic programs to be sets of sentences of an abstract logic. When these abstract logics possess certain logical properties (some properties considered are compactness, finitariness, and monotone consequence relations) we show how to develop a fixed-point, model-state-theoretic and proof theoretic semantics for such programs. The work of Melvin Fitting on developing a generalized semantics for multivalued logic programming is extended here to arbitrary abstract logics. We present examples to show how our semantics is robust enough to be applicable to various non-classical logics like temporal logic and multivalued logics, as well as to extensions of classical logic programming such as disjunctive logic programming. We also show how some aspects of the declarative semantics of distributed logic programming, particularly work of Ramanujam, can be incorporated into our framework

Set of support, demodulation, paramodulation: a historical perspective

This article is a tribute to the scientific legacy of automated reasoning pioneer and JAR founder Lawrence T. (Larry) Wos. Larry's main technical contributions were the set-of-support strategy for resolution theorem proving, and the demodulation and paramodulation inference rules for building equality into resolution. Starting from the original definitions of these concepts in Larry's papers, this survey traces their evolution, unearthing the often forgotten trails that connect Larry's original definitions to those that became standard in the field