Super Logic Programs

The Autoepistemic Logic of Knowledge and Belief (AELB) is a powerful nonmonotic formalism introduced by Teodor Przymusinski in 1994. In this paper, we specialize it to a class of theories called `super logic programs'. We argue that these programs form a natural generalization of standard logic programs. In particular, they allow disjunctions and default negation of arbibrary positive objective formulas. Our main results are two new and powerful characterizations of the static semant ics of these programs, one syntactic, and one model-theoretic. The syntactic fixed point characterization is much simpler than the fixed point construction of the static semantics for arbitrary AELB theories. The model-theoretic characterization via Kripke models allows one to construct finite representations of the inherently infinite static expansions. Both characterizations can be used as the basis of algorithms for query answering under the static semantics. We describe a query-answering interpreter for super programs which we developed based on the model-theoretic characterization and which is available on the web.Comment: 47 pages, revised version of the paper submitted 10/200

Static Semantics For Normal and Disjunctive Logic Programs

In this paper, we propose a new semantic framework for disjunctive logic programming by introducing static expansions of disjunctive programs. The class of static expansions extends both the classes of stable, well-founded and stationary models of normal programs and the class of minimal models of positive disjunctive programs. Any static expansion of a program P provides the corresponding semantics for P consisting of the set of all sentences logically implied by the expansion. We show that among all static expansions of a disjunctive program P there is always the least static expansion which we call the static completion P of P . The static completion P can be defined as the least fixed point of a natural minimal model operator and can be constructed by means of a simple iterative procedure. The semantics defined by the static completion P is called the static semantics of P . It coincides with the set of sentences that are true in all static expansions of P . For normal programs, i..

Well-Founded and Stationary Models of Logic Programs

Machine (XWAM) for this semantics [War89] and developed an elegant interpreter in Prolog [CW92]. For datalog programs with negation, the computation of well-founded models is quadratic in the size of the program [VGRS90]. Moreover, the well-founded semantics is always cumulative [Dix91, LY91]. 3.6 Partial Stable or Stationary Models Stable and well-founded semantics are closely related. In [Prz90, Prz91c] the author introduced partial stable models of normal logic programs, which were later renamed stationary models [Prz91b]. Partial stable (or stationary) models constitute a natural generalization of the (total) stable models and are defined as fixed points of a program transformation (factorization) which is analogous to the transformation used in the original definition of stable models [GL88]. It turns out that the wellfounded model always coincides with the smallest partial stable model and thus every normal logic program P has at least one partial stable model. It also follows ..

Two Simple Characterizations of Well-Founded Semantics

this paper we show that well-founded models can also be defined as fixed points of a natural program transformation (factorization) which is completely analogous to the transformation used in the definition of stable models and is expressed entirely in terms of classical, 2-valued logic. Subsequently, we use this result to provide a constructive definition of well-founded models as fixed points of an iterative factorization procedure. We note that no such constructive characterization is available for stable models which are computationally intractable even in the class of propositional programs [KS89, MT88]. The results obtained in this paper, coupled with our earlier result showing that the wellfounded semantics can be equivalently defined by means of first order completions of logic programs [Prz91c], provide natural and simple characterizations of well-founded semantics, given entirely in terms of classical, 2-valued logic and thus, hopefully, dispel some of th

Semantics of Normal and Disjunctive Logic Programs A Unifying Framework

. We introduce a simple uniform semantic framework that isomorphically contains major semantics proposed recently for normal, disjunctive and extended logic programs, including the perfect model, stable, well-founded, disjunctive stable, stationary and static semantics and many others. The existence of such a natural framework allows us to compare major proposed semantics, analyze their properties, provide simpler definitions and generate new semantics satisfying a specific set of conditions. 1 Introduction Various semantics have been recently proposed for normal, disjunctive and extended logic programs, including 1 the following: -- Perfect model semantics [ABW88, VG89, Prz88] and disjunctive perfect model semantics [Prz88]. -- Stable semantics [GL88, BF91] and disjunctive stable semantics [GL90, Prz91b]. -- Well-founded semantics [VGRS90]. -- Partial stable semantics [Prz90] and disjunctive partial stable semantics [Prz91b]. -- Stationary semantics [Prz91c]. -- Static seman..

Non-Monotonic Formalisms And Logic Programming

this paper is to discuss recent research developments, whic

A Knowledge Representation Framework Based on Autoepistemic Logic of Minimal Beliefs

In recent years, various formalizations of nonmonotonic reasoning and different semantics for normal and disjunctive logic programs have been proposed, including autoepistemic logic, circumscription, CWA, GCWA, ECWA, epistemic specifications, stable, well-founded, stationary and static semantics of normal and disjunctive logic programs. In this paper we introduce a simple nonmonotonic knowledge representation framework which isomorphically contains all of the above mentioned non-monotonic formalisms and semantics as special cases and yet is significantly more expressive than each one of these formalisms considered individually. The new formalism, called the AutoEpistemic Logic of minimal Beliefs, AELB, is obtained by augmenting Moore's autoepistemic logic, AEL, with an additional minimal belief operator, B, which allows us to explicitly talk about minimally entailed formulae. The existence of such a uniform framework not only results in a new powerful non-monotonic formalism but al..

On the Declarative and Procedural Semantics of Logic Programs

One of the most important and difficult problems in logic programming is the problem of finding a suitable declarative or intended semantics for logic programs. The importance of this problem stems from the declarative character of logic programming, whereas its difficulty can be largely attributed to the non-monotonic character of the negation operator used in logic programs. The problem can therefore be viewed as the problem of finding a suitable formalization of the type of non-monotonic reasoning used in logic programming. In this paper we introduce a semantics of logic programs based on the class PERF(P) of all, not necessarily Herbrand, perfect models of a program P and we show that the proposed semantics is not only natural but it also combines many of the desirable features of previous approaches, at the same time eliminating some of their drawbacks. For a positive program P, the class PERF(P) of perfect models coincides with the class MIN(P) of all minimal models of P. The per..

Autoepistemic Logics of Closed Beliefs and Logic Programming

Moore's autoepistemic logic AEL proved to be a very successful approach to formalizing non-monotonic reasoning and logic programming. However, AEL also has some important drawbacks, e.g., quite "reasonable" theories are often inconsistent in AEL, it does not always lead to the expected, intended semantics and it cannot be effectively computed even for very simple classes of theories. In this paper we propose a more general approach to autoepistemic reasoning by introducing Autoepistemic Logics of Closed Beliefs AEL cl , where j= cl denotes a specific negative introspection inference operator ("closed world assumption") on which negative introspection in this logic is based. Negative introspection determines which formulae in autoepistemic logic are disbelieved, or, putting it differently, negation of which formulae can be assumed by default. It determines therefore the set of closed world beliefs derivable in a given autoepistemic logic. Moore's autoepistemic logic AEL is a specia..

Autoepistemic Logic of Knowledge and Beliefs

In recent years, various formalizations of non-monotonic reasoning and different semantics for normal and disjunctive logic programs have been proposed, including autoepistemic logic, circumscription, CWA, GCWA, ECWA, epistemic specifications, stable, well-founded, stationary and static semantics of normal and disjunctive logic programs. In this paper we introduce a simple non-monotonic knowledge representation framework which isomorphically contains all of the above mentioned non-monotonic formalisms and semantics as special cases and yet is significantly more expressive than each one of these formalisms considered individually. The new formalism, called the Autoepistemic Logic of Knowledge and Beliefs, AELB, is obtained by augmenting Moore's autoepistemic logic, AEL, already employing the knowledge operator , L, with an additional belief operator , B. As a result, we are able to reason not only about formulae F which are known to be true (i.e., those for which LF holds) but also abou..