459 research outputs found
Variations on a Theme: A Bibliography on Approaches to Theorem Proving Inspired From Satchmo
This articles is a structured bibliography on theorem provers,
approaches to theorem proving, and theorem proving applications inspired
from Satchmo, the model generation theorem prover developed
in the mid 80es of the 20th century at ECRC, the European Computer-
Industry Research Centre. Note that the bibliography given in this article
is not exhaustive
Nested sequent calculi and theorem proving for normal conditional logics: The theorem prover NESCOND
Implementing semantic tableaux
This report describes implementions of the tableau calculus for
first-order logic. First an extremely simple implementation,
called leanTAP, is presented, which nonetheless covers the full
functionality of the calculus and is also competitive with respect
to performance. A second approach uses compilation techniques for
proof search. Improvements inculding universal variables and
lemmata are considered as well as more efficient data structures
using reduced ordered binary decision diagrams. The implementation
language is PROLOG. In all cases fully operational PROLOG code is
given. For leanTAP a formal proof of the correctness of the
implementation is given relying on the operational semantics of
PROLOG as given by the SLD-tree model.
This report will appear as a chapter in the
Handbook of Tableau-based Methods in Automated Deduction
edited by: D. Gabbay, M. D\u27Agostino, R. H\"{a}hnle, and
J.Posegga
published by: KLUWER ACADEMIC PUBLISHERS
Electronic availability will be discontinued after final acceptance
for publication is obtained
Satisfiability Calculus: An Abstract Formulation of Semantic Proof Systems
The theory of institutions, introduced by Goguen and Burstall in 1984, can be thought of as an abstract formulation of model theory. This theory has been shown to be particularly useful in computer science, as a mathematical foundation for formal approaches to software construction. Institution theory was extended by a number of researchers, José Meseguer among them, who, in 1989, presented General Logics, wherein the model theoretical view of institutions is complemented by providing (categorical) structures supporting the proof theory of any given logic. In other words, Meseguer introduced the notion of proof calculus as a formalisation of syntactical deduction, thus ?implementing? the entailment relation of a given logic. In this paper we follow the approach initiated by Goguen and introduce the concept of Satisfiability Calculus. This concept can be regarded as the semantical counterpart of Meseguer?s notion of proof calculus, as it provides the formal foundations for those proof systems that resort to model construction techniques to prove or disprove a given formula, thus ?implementing? the satisfiability relation of an institution. These kinds of semantic proof methods have gained a great amount of interest in computer science over the years, as they provide the basic means for many automated theorem proving techniques.Fil: Lopez Pombo, Carlos Gustavo. Consejo Nacional de Investigaciones CientÃficas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigación en Ciencias de la Computación. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigación en Ciencias de la Computación; ArgentinaFil: Castro, Pablo. Universidad Nacional de RÃo Cuarto. Facultad de Ciencias Exactas FisicoquÃmicas y Naturales. Departamento de Computación; ArgentinaFil: Aguirre, Nazareno M.. Universidad Nacional de RÃo Cuarto. Facultad de Ciencias Exactas FisicoquÃmicas y Naturales. Departamento de Computación; ArgentinaFil: Maibaum, Thomas S.E.. Mc Master University; Canad
Proof Theory of Finite-valued Logics
The proof theory of many-valued systems has not been investigated to an extent comparable to the work done on axiomatizatbility of many-valued logics. Proof theory requires appropriate formalisms, such as sequent calculus, natural deduction, and tableaux for classical (and intuitionistic) logic. One particular method for systematically obtaining calculi for all finite-valued logics was invented independently by several researchers, with slight variations in design and presentation. The main aim of this report is to develop the proof theory of finite-valued first order logics in a general way, and to present some of the more important results in this area. In Systems covered are the resolution calculus, sequent calculus, tableaux, and natural deduction. This report is actually a template, from which all results can be specialized to particular logics
Proof search in constructive logics
We present an overview of some sequent calculi organised not for
"theorem-proving" but for proof search, where the proofs themselves
(and the avoidance of known proofs on backtracking) are objects of
interest. The main calculus discussed is that of Herbelin [1994] for
intuitionistic logic, which extends methods used in hereditary
Harrop logic programming; we give a brief discussion of similar
calculi for other logics. We also point out to some related work on
permutations in intuitionistic Gentzen sequent calculi that
clarifies the relationship between such calculi and natural
deduction.Centro de Matemática da Universidade do Minho (CMAT).União Europeia (UE) - Programa ESPRIT - BRA 7232 Gentzen
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