Expressing preferences in logic programming using an infinite-valued logic

Abstract

We propose the new logic programming language PrefLog, which is based on an infinite-valued logic in order to support operators for expressing preferences. We demonstrate that if the operators used are continuous over the infinite-valued underlying domain, then the resulting logic programming language retains the well-known properties of classical logic programming (and most notably the existence of a least Herbrand model). We argue that one can define simple and natural new continuous operators by using a small set of operators that are easily shown to be continuous. Finally, we demonstrate that despite the fact that the underlying truth domain and the set of possible interpretations of a PrefLog program are infinite, we can define a terminating bottom-up proof procedure for implementing a significant and useful fragment of the language.

Lexicographic Logic: a Many-valued Logic for Preference Representation

“…-The flexible queries approach described in [10] that is based on possibilistic logic [11]. -The infinite-valued approach proposed in [1,2] and extended in the context of logic programming in [19].…”

“…The semantics of this query language is based on the infinite-valued logic introduced in [20]. The language was subsequently extended with recursion obtaining the logic programming language PrefLog [19]. The infinite-valued approach shares a similar philosophy with lexicographic logic: preferences are expressed implicitly using operators in the context of many-valued logics.…”

“…During the past three decades, many formalisms have been developed for representing preferences, both in artificial intelligence [9] as-well-as in databases [22]. Of particular interest are the logical approaches in which the specification of preferences is performed using operators that implicitly manipulate the underlying preference values [5,7,2,16,10,19,8]. Such formalisms are usually declarative, concise, and easy to understand and reason about.…”

Extensions of logic programming for preference representation

“…In order to formulate this approach [62,63] we introduce the logic programming language PrefLog, its syntax, and its semantics; in particular, we study the properties of the Pre-fLog operators that are needed in order for the PrefLog programs to behave well from a semantic point of view. In addition, we introduce a bottom-up evaluation method for a well-defined class of function-free PrefLog programs.…”