Topic
Classical logic
About: Classical logic is a research topic. Over the lifetime, 3622 publications have been published within this topic receiving 80138 citations. The topic is also known as: standard logic.
Papers published on a yearly basis
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Papers
TL;DR: It is shown that some facts of commonsense knowledge can be represented by logic programs and disjunctive databases more easily when classical negation is available.
Abstract: An important limitation of traditional logic programming as a knowledge representation tool, in comparison with classical logic, is that logic programming does not allow us to deal directly with incomplete information. In order to overcome this limitation, we extend the class of general logic programs by including classical negation, in addition to negation-as-failure. The semantics of such extended programs is based on the method of stable models. The concept of a disjunctive database can be extended in a similar way. We show that some facts of commonsense knowledge can be represented by logic programs and disjunctive databases more easily when classical negation is available. Computationally, classical negation can be eliminated from extended programs by a simple preprocessor. Extended programs are identical to a special case of default theories in the sense of Reiter.
2,615 citations
TL;DR: This paper is primarily concerned with a special case of one of the leading problems of mathematical logic, the problem of finding a regular procedure to determine the truth or falsity of any given logical formula.
Abstract: This paper is primarily concerned with a special case of one of the leading problems of mathematical logic, the problem of finding a regular procedure to determine the truth or falsity of any given logical formula*. But in the course of this investigation it is necessary to use certain theorems on combinations which have an independent interest and are most conveniently set out by themselves beforehand.
2,512 citations
1 Jan 1977
TL;DR: It is argued that a sophisticated question-answering machine that has the capability of making inferences from its data base should employ a certain four-valued logic, the motivating consideration being that minor inconsistencies in its data should not be allowed to lead to irrelevant conclusions.
Abstract: It is argued that a sophisticated question-answering machine that has the capability of making inferences from its data base should employ a certain four-valued logic, the motivating consideration being that minor inconsistencies in its data should not be allowed to lead (as in classical logic) to irrelevant conclusions. The actual form of the four-valued logic is ‘deduced’ from an interplay of this motivating consideration with certain ideas of Dana Scott concerning ‘approximation lattices.’
1,656 citations
TL;DR: In this paper, a theory of algebraic systems that would correspond in a natural fashion to the No-valued propositional calculus was developed, where MV is supposed to suggest many-valued logics.
Abstract: This paper is an attempt at developing a theory of algebraic systems that would correspond in a natural fashion to the No-valued propositional calculus(2). For want of a better name, we shall call these algebraic systems MV-algebras where MV is supposed to suggest many-valued logics. It is known that the classical two-valued logic gives rise to the study of Boolean algebras and, as can be expected, every Boolean algebra will be an MValgebra whereas the converse does not hold. However, many results for Boolean algebras can be appropriately carried over to MV-algebras, although in some cases the proofs become more subtle and delicate. The motivation behind the present study is to find a proof of the completeness of the Novalued logic by using some algebraic results concerning MV-algebras; more specifically, it is known that the completeness of the two-valued logic is a consequence of the Boolean prime ideal theorem and we wish to exploit just some such corresponding result for MV-algebras(3). It will be seen that our effort in duplicating this result is only partially successful. In the first four sections of this paper we present various theorems concerning both the arithmetic in MV-algebras and the structure of these algebras. In the last section we give some applications of our results to the study of completeness of NO-valued logic and some related topics. We point out here that the treatment of MV-algebras as given here is not meant to be complete and exhaustive. 1. Axioms of MV-algebras and some elementary consequences. An MV
1,492 citations
TL;DR: A model and proof theories, a proof procedure, and applications for one non-monotonic logic are developed, and it is proved the completeness of the non-Monotonic predicate calculus and the decidability of theNon- monotonic sentential calculus.
1,063 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2025 | 3 |
| 2024 | 7 |
| 2023 | 14 |
| 2022 | 53 |
| 2021 | 91 |
| 2020 | 76 |