Reducing fuzzy answer set programming to model finding in fuzzy logics

Abstract

In recent years answer set programming has been extended to deal with multi-valued predicates. The resulting formalisms allows for the modeling of continuous problems as elegantly as ASP allows for the modeling of discrete problems, by combining the stable model semantics underlying ASP with fuzzy logics. However, contrary to the case of classical ASP where many efficient solvers have been constructed, to date there is no efficient fuzzy answer set programming solver. A well-known technique for classical ASP consists of translating an ASP program P to a propositional theory whose models exactly correspond to the answer sets of P . In this paper, we show how this idea can be extended to fuzzy ASP, paving the way to implement efficient fuzzy ASP solvers that can take advantage of existing fuzzy logic reasoners.

Stable Models of Fuzzy Propositional Formulas

“…Note that this example, like Example 5, uses nested connectives, such as ¬ s ¬ s , that are not available in previous fuzzy ASP semantics, such as [2,3].…”

“…While they do not subsume each other, it is clear that many real-world problems require both their strengths. This led to the body of work on combining fuzzy logic and the stable model semantics, known as fuzzy answer set programming (e.g., [2][3][4][5][6][7][8][9]). However, most work considers simple rule forms and do not allow connectives nested arbitrarily as in fuzzy logic.…”

Local search and restart strategies for satisfiability solving in fuzzy logics

“…Indeed, many fuzzy reasoning tasks can be reduced to SAT ∞ , including reasoning about vague concepts in the context of the semantic web [4], fuzzy spatial reasoning [5] and fuzzy answer set programming [6], which in itself is an important framework for non-monotonic reasoning over continuous domains (see e.g. [7], [8], [9]).…”

Solving satisfiability in fuzzy logics by mixing CMA-ES

“…Like its classical counterpart, it is useful for solving a variety of problems. Indeed, many fuzzy reasoning tasks can be reduced to SAT∞, including reasoning about vague concepts in the context of the semantic web [11], fuzzy spatial reasoning [9] and fuzzy answer set programming [7], which in itself is an important framework for non-monotonic reasoning over continuous domains (see e.g. [8,13]).…”