The first Hilbert style formalization of the intuitionistic logic, formulated as a proof system, is due to A. Heyting (1930). In this chapter we present a Hilbert style proof system I that is equivalent to the Heyting's original formalization and discuss the relationship between intuitionistic ...
Modern categorical logic as well as the Kripke and topological models of intuitionistic logic suggest that the interpretation of ordinary "propositional" logic should in general be the logic of subsets of a given universe set. Partitions on a set are dual to subsets of a set in the sense of ...
In Part I, they show that typed lambda-calculi, a formulation of higher order logic, and cartesian closed categories are essentially the same. In Part II, it is demonstrated that another formulation of higher order logic (intuitionistic t... (展开全部) 喜欢读"Introduction to Higher-Order ...
The main aim of fuzzy logic and fuzzy sets is to overcome the disadvantages of classical logic and classical sets.This is a preview of subscription content, log in via an institution to check access. References Atanassov K (1986) Intuitionistic fuzzy sets. Fuzzy Sets Syst 20:87–96 Google ...
It refers to the objects of mathematical knowledge, to the knowledge itself, to the methods used to acquire and represent this knowledge, to the language of mathematics, to the role and nature of logic in its relation to mathematics, to the institutions that accompany mathematics, to the ...
The idea of interpreting types as structured objects, rather than sets, has a long pedigree, and is known to clarify various mysterious aspects of type theory. For instance, interpreting types as sheaves helps explain the intuitionistic nature of type-theoretic logic, while interpreting them as par...
[28] introduced some arithmetic operations and logic operators for TIFNs and incorporated these into the fault analysis of a system while [23] defined some arithmetic operations on Trapezoidal Intuitionistic Fuzzy Numbers (TRIFN) and evaluated the fuzzy reliability using these operations. [7] ...
In Part I, they show that typed lambda-calculi, a formulation of higher-order logic, and cartesian closed categories, are essentially the same. Part II demonstrates that another formulation of higher-order logic, (intuitionistic) type theories, is closely related to topos theory. Part III is ...
In Part I, they show that typed lambda-calculi, a formulation of higher-order logic, and cartesian closed categories, are essentially the same. Part II demonstrates that another formulation of higher-order logic, (intuitionistic) type theories, is closely related to topos theory. Part III is ...
In the mid-1980s researchers in the computer science and artificial intelligence communities began to take an interest in logics studied by logicians and philosophers since at least Aristotle in the fourth century BC. These are logics such as deontic, epistemic, intuitionistic, modal, ...