Introduction to higher order categorical logic
Introduction to higher order categorical logic
Linear logic: its syntax and semantics
Proceedings of the workshop on Advances in linear logic
Short note: on the redundancy of axiom (A3) in BL and MTL
Soft Computing - A Fusion of Foundations, Methodologies and Applications
A categorical semantics for fuzzy predicate logic
Fuzzy Sets and Systems
When does a category built on a lattice with a monoidal structure have a monoidal structure?
Fuzzy Sets and Systems
A non-commutative and non-idempotent theory of quantale sets
Fuzzy Sets and Systems
Nuclei and conuclei on residuated lattices
Fuzzy Sets and Systems
Fuzzy presubsets as non-idempotent and non-commutative classifications of subalgebras
Fuzzy Sets and Systems
Q-fuzzy subsets on ordered semigroups
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.