Since Chang [2] introduced fuzzy theory into topology, many authors have discussed various aspects of fuzzy topology. It is well known that weakly induced and induced topological spaces play an important role in L-topological spaces (see book [8]). According to their value ranges, L-topological spaces form different categories. Clearly, the investigation on their relationships is certainly impo...

We extend the ordinary concept of theory morphism in institutions to extra theory morphisms. Extra theory morphism map theories belonging to different institutions across institution morphisms. We investigate the basic mathematical properties of extra theory morphisms supporting the semantics of logical multiparadigm languages, especially structuring specifications (module systems) á la OBJ-Cle...

This chapter introduces context algebras and demonstrates their application to combining logical and vector-based representations of meaning. Other chapters in this volume consider approaches that attempt to reproduce aspects of logical semantics within new frameworks. The approach we present here is different: We show how logical semantics can be embedded within a vector space framework, and u...

This paper aims to formally define a concept of interpretability according to natural language of a logical theory, and show advances for demonstrating that the logic system called Compensatory Fuzzy Logic is interpretable. A logical theory is interpretable according to natural language if the calculus based upon the elements of this logical theory can be understood in natural language and vice...

Possibilistic logic in general [7, 8, 9, 10] investigates how possibilistic uncertainty about propositions is propagated when making inferences in a formal logical system. In this paper, we look at a very particular aspect of possibilistic logic: we investigate how, under certain independence assumptions, the introduction of possibilistic uncertainty in classical propositional logic leads to th...

Research on conjoint analysis/preference aggregation/social choice aggregation is performed by more than forty years by various communities. However, many proposed mathematical models understand preferences as irreflexive, transitive and statical relations while there is human psychology research work questioning these properties as being not enough motivated. This works propose to position the...

We describe an automatic approach for evaluating interpretability of fuzzy rule-based classifiers. The approach is based on the logical view of fuzzy rules, which are interpreted as rows in truth tables. These truth tables are subject of a minimization procedure based on a variant of the Quine-McCluskey algorithm. The minimized truth tables are used to build new fuzzy rules, which are compared ...

Provably correct compilation is an important aspect in development of high assurance software systems. In this paper we present an approach to provably correct compilation based on Horn logical semantics of programming languages and partial evaluation. We also show that continuation semantics can be expressed in the Horn logical framework, and introduce Definite Clause Semantics. We illustrate ...

Provably correct compilation is an important aspect in development of high assurance software systems. In this paper we explore approaches to provably correct code generation based on programming language semantics, particularly Horn logical semantics, and partial evaluation. We show that the definite clause grammar (DCG) notation can be used for specifying both the syntax and semantics of impe...