Algebraic logic

AN ALGEBRAIC STRUCTURE FOR INTUITIONISTIC FUZZY LOGIC

In this paper we extend the notion of  degrees of membership and non-membership of intuitionistic fuzzy sets to lattices and  introduce a residuated lattice with appropriate operations to serve as semantics of intuitionistic fuzzy logic. It would be a step forward to find an algebraic counterpart for intuitionistic fuzzy logic. We give the main properties of the operations defined and prove som...

an algebraic structure for intuitionistic fuzzy logic

in this paper we extend the notion of  degrees of membership and non-membership of intuitionistic fuzzy sets to lattices and  introduce a residuated lattice with appropriate operations to serve as semantics of intuitionistic fuzzy logic. it would be a step forward to find an algebraic counterpart for intuitionistic fuzzy logic. we give the main properties of the operations defined and prove som...

Algebraic Logic : Referential Algebraic Semantics

Wójcicki has provided a characterization of selfextensional logics as those that can be endowed with a complete local referential semantics. His result was extended by Jansana and Palmigiano, who developed a duality between the category of reduced congruential atlases and that of reduced referential algebras over a fixed similarity type. This duality restricts to one between reduced atlas model...

Applying Algebraic Logic

Algebraic Neighbourhood Logic

We present an algebraic embedding of Neighbourhood Logic (NL) into the framework of semirings which yields various simplifications. For example, some of the NL axioms can be dropped, since they are theorems in our framework, and Galois connections produce properties for free. A further simplification is achieved, since the semiring methods used are easy and fairly standard. Moreover, this embed...