In this chapter, we consider particular classes of infinite-valued propositional logics which are strongly related to t-norms as conjunction connectives and to the real unit interval as set of their truth degrees, and which have their implication connectives determined via an adjointness condition. Such systems have in the last ten years been of considerable interest, and the topic of important...

Fuzzy Description Logics (DLs) can be used to represent and reason with vague knowledge. This family of logical formalisms is very diverse, each member being characterized by a specific choice of constructors, axioms, and triangular norms, which are used to specify the semantics. Unfortunately, it has recently been shown that the consistency problem in many fuzzy DLs with general concept inclus...

Statistical learning approaches, bounded mainly to knowledge related to perceptual manifestations of semantics, fall short to adequately utilise the meaning and logical connotations pertaining to the extracted image semantics. Instigated by the Semantic Web, ontologies have appealed to a significant share of synergistic approaches towards the combined use of statistical learning and explicit se...

Abstract Weighted knowledge bases for description logics with typicality have been recently considered under a “concept-wise” multipreference semantics (in both the two-valued and fuzzy case), as basis of logical multilayer perceptrons (MLPs). In this paper we consider weighted conditional $\mathcal{ALC}$ in finitely many-valued case, through three different semantic constructions. For boolean ...

We deene a simple logical semantics based on minimal models in Lukasiewicz's 3-valued logic, L 3. On normal logic programs it is equivalent to the well-founded semantics (WFS), and on disjunctive programs it is equivalent to the P-stable semantics of Eiter, Leone and Saccc a, hence to Przymusinski's 3-valued stable semantics. One advantage is that it is char-acterised by simple conditions on mo...

In this chapter, we present a tutorial about fuzzy answer set programming (FASP); we give a gentle introduction to its basic ideas and definitions. FASP is a combination of answer set programming and fuzzy logics which has recently been proposed. From the answer set semantics, FASP inherits the declarative nonmonotonic reasoning capabilities, while fuzzy logic adds the power to model continuous...

Let Gm be the m-valued Gödel-Dummett fuzzy logic. If m ≥ 3 then neither conjunction nor implication is in Gm expressible in terms of the remaining connectives. This fact remains true even if the propositional language is enriched by propositional constants for all truth values. Gödel-Dummett fuzzy propositional logic can be defined as an extension of the intuitionistic propositional logic by th...

During the past decade, knowledge representation research in AI has generated a class of languages called term subsumption languages (TSL), which is a knowledge representation formalism with a well-defined logic-based semanticsDue to its formal semantics, a term subsumption system can automatically infer the subsumption relationships between concepts defined in the system. However, these system...