Topic
Intuitionistic logic
About: Intuitionistic logic is a research topic. Over the lifetime, 3189 publications have been published within this topic receiving 63614 citations. The topic is also known as: constructive logic.
Papers published on a yearly basis
1 / 2
Papers
Book•
21 Sep 2019
TL;DR: In this chapter, the basic definitions and properties of the interval valued intuitionistic fuzzy sets (IVIFSs) will be introduced and the majority of the proofs below are analogous to the proofs from Chapter 1.
Abstract: In this chapter, the basic definitions and properties of the interval valued intuitionistic fuzzy sets (IVIFSs) will be introduced. We will omit the majority of the proofs below, which are, in general, analogous to the proofs from Chapter 1.
2,276 citations
Book Chapter•
1 Jan 1999
TL;DR: The author makes an introduction to non-standard analysis, then extends the dialectics to neutrosophy which became a new branch of philosophy, which is the first logic that comprises paradoxes and distinguishes between relative and absolute truth.
Abstract: The author makes an introduction to non-standard analysis, then extends the dialectics to neutrosophy which became a new branch of philosophy. This new concept helps in generalizing the intuitionistic, paraconsistent, dialetheism, fuzzy logic to neutrosophic logic which is the first logic that comprises paradoxes and distinguishes between relative and absolute truth. Similarly, the fuzzy set is generalized to neutrosophic set. Also, the classical and imprecise probabilities are generalized to neutrosophic probability.
1,147 citations
Book•
30 Apr 1983
TL;DR: In this paper, the authors present a survey of analytical modal tableaus and consistent properties of these modalities, including logical consequence, compactness, interpolation, and other topics.
Abstract: One / Background.- Two / Analytic Modal Tableaus and Consistency Properties.- Three / Logical Consequence, Compactness, Interpolation, and Other Topics.- Four / Axiom Systems and Natural Deduction.- Five / Non-Analytic Logics.- Six / Non-Normal Logics.- Seven / Quantifiers.- Eight / Prefixed Tableau Systems.- Nine / Intuitionistic Logic.- Special Notation.
816 citations
Book•
15 Aug 1988
TL;DR: In this article, the authors present a theory of Intuitionistic Logic and Constructive Set Theory with Sheaves, Sites and Higher Order Logic, and apply it to algebra, algebraic geometry and higher order logic.
Abstract: 7. The Topology of Metric Spaces. 8. Algebra. 9. Finite Type Arithmetic and Theories of Operators. 10. Proof Theory of Intuitionistic Logic. 11. The Theory of Types and Constructive Set Theory. 12. Choice Sequences. 13. Semantical Completeness. 14. Sheaves, Sites and Higher Order Logic. 15. Applications of Sheaf Models. 16. Epilogue. Bibliography. Index.
732 citations
TL;DR: In this paper, a semantical analysis of intuitionistic logic I is presented and a model theory for intuitionistic predicate logic is presented. Butler et al. present a decision procedure for logic I.
Abstract: Publisher Summary The chapter discusses a semantical analysis of intuitionistic logic I. The chapter presents a semantical model theory for Heyting's intuitionist predicate logic and proves the completeness of that system relative to the modeling. The semantics for modal logic that is announced and developed together with the known mappings of intuitionistic logic into the modal system, S4, inspired the present semantics for intuitionist logic. It is important to develop the semantics of intuitionistic logic independently of that of S4; this procedure helps to obtain somewhat more information about intuitionistic logic, including the mapping into S4 as a consequence thereof. In addition to giving a simple decision procedure for Heyting's propositional calculus, the chapter presents the undecidability of monadic intuitionistic quantification theory. The proof is based on the semantics previously developed. Beth semantic tableaux for intuitionistic logic is developed in the chapter. The chapter describes consistency property: in a standard formalization of Heyting's predicate calculus, the axioms are all valid, and the rules preserve validity.
678 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2025 | 13 |
| 2024 | 13 |
| 2023 | 40 |
| 2022 | 96 |
| 2021 | 76 |
| 2020 | 69 |