A categorical semantics for fuzzy predicate logic

Stout, Lawrence Neff

doi:10.1016/j.fss.2009.09.007

Cited by 4 publications

(3 citation statements)

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“…Categorical semantics for first order logic is covered extensively in [22], so I will be brief here and concentrate on a sequent calculus related to the logic given by the rules for deduction given above (which have more of the character of natural deduction).…”

Section: Categorical Semantics 01 Non-commutative Propositional Logicmentioning

confidence: 99%

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Categorical approaches to non-commutative fuzzy logic

Stout

2010

Fuzzy Sets and Systems

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In this paper we consider what it means for a logic to be non-commutative, how to generate examples of structures with a non-commutative operation * which have enough nice properties to serve as the truth values for a logic. Inference in the propositional logic is gotten from the categorical properties (products, coproducts, monoidal and closed structures, adjoint functors) of the categories of truth values. We then show how to extend this view of propositional logic to a predicate logic using categories of propositions about a type A with functors giving change of type and adjoints giving quantifiers. In the case where the semantics takes place in Set (L) (Goguen's category of L-fuzzy sets), the categories of predicates about A can be represented as internal category objects with the quantifiers as internal functors.

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Section: Categorical Semantics 01 Non-commutative Propositional Logicmentioning

confidence: 99%

“…As mentioned earlier and developed at length in [22] a categorical form of semantics for predicate calculus takes this picture and spreads it out over a category of types:…”

Section: Predicate Logic With Non-commutative *mentioning

confidence: 99%

Categorical approaches to non-commutative fuzzy logic

Stout

2010

Fuzzy Sets and Systems

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“…After this, fuzzy set theory becomes the base of fuzzy computing systems. On this basis, researchers have combined it with knowledge representation and reasoning methods in artificial intelligence, such as fuzzy production rules [11], fuzzy Petri nets [12], fuzzy neural network [13], fuzzy predicate [14], etc. So far, fuzzy set theory has been widely and maturely used in many areas.…”

Section: Introductionmentioning

confidence: 99%

Knowledge representation using fuzzy spiking neural P system

Wang

Peng

et al. 2010

2010 IEEE Fifth International Conference on Bio-Inspired Computing: Theories and Applications (BIC-TA)

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This paper presents a fuzzy spiking neural P system (FSN P system) to represent the fuzzy production rules in a knowledge base of a rule-based system, where the certainty fac tors of fuzzy production rules and the truth values of propositions are described by trapezoidal fuzzy numbers. In the proposed FSN P system, the definition of traditional neurons has been extended.The neurons are divided into two types: proposition neurons and rule neurons; the content of each neuron is a trapezoidal fuzzy number in [0,1] instead of an integer. Also the fuzzy reasoning process can be modeled by the proposed FSN P system.

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