Stable Models of Fuzzy Propositional Formulas

Abstract. We introduce the stable model semantics for fuzzy propositional for-mulas, which generalizes both fuzzy propositional logic and the stable model se-mantics of Boolean propositional formulas. Combining the advantages of both for-malisms, the introduced language allows highly configurable default reasoning in-volving fuzzy truth values. We show that several properties of Boolean stable mod-els are naturally extended to this formalism, and discuss how it is related to other approaches to combining fuzzy logic and the stable model semantics.

Query Answering in Normal Logic Programs under Uncertainty

We present a simple, yet general top-down query answering procedure for normal logic programs over lattices and bilattices, where functions may appear in the rule bodies. Its interest relies on the fact that many approaches to paraconsistency and uncertainty in logic programs with or without non-monotonic negation are based on bilattices or lattices, respectively

MWeb: A principled framework for modular web rule bases and its semantics

We present a principled framework for modular web rule bases, called MWeb. According to this framework, each predicate defined in a rule base is characterized by its defining reasoning mode, scope, and exporting rule base list. Each predicate used in a rule base is characterized by its requesting reasoning mode and importing rule base list. For legal MWeb modular rule bases S, the MWebAS and MWebWFS semantics of each rule base s ∈ S w.r.t. S are defined model-theoretically. These semantics extend the answer set semantics (AS) and the well-founded semantics with ex- plicit negation (WFSX) on ELPs, respectively, keeping all of their semantical and computational characteristics. Our framework supports: (i) local semantics and different points of view, (ii) local closed-world and open-world assumptions, (iii) scoped negation-as-failure, (iv) restricted propa- gation of local inconsistencies, and (v) monotonicity of reasoning, for “fully shared” predicates