Considerations on Updates of Logic Programs

Abstract

Abstract. Among others, Alferes et al. (1998) presented an approach for updating logic programs with sets of rules based on dynamic logic programs. We syntactically redefine dynamic logic programs and investigate their semantical properties, looking at them from perspectives such as a belief revision and abstract consequence relation view. Since the approach does not respect minimality of change, we refine its stable model semantics and present minimal stable models and strict stable models. We also compare the update approach to related work, and find that is equivalent to a class of inheritance programs independently defined by Buccafurri et al. (1999).

Reasoning about Evolving Nonmonotonic Knowledge Bases

“…We sometimes use ∪P to denote the set of all rules occurring in P, i.e., ∪P = n i=1 P i . The semantics of update programs can abstractly be described in terms of a belief operator Bel(·), which associates with every sequence P a set Bel(P) ⊆ L A of rules, intuitively viewed as the consequences of P. Bel(·) may be instantiated in terms of various proposals for update semantics, like, e.g., the approaches described in [2,34,21,13,28].…”

“…For concrete examples, we consider the answer set semantics for propositional update programs as introduced in [13,14], as well as the semantics for dynamic logic programs as defined in [2,25]. The former semantics defines answer sets of a sequence of ELPs, P = (P 0 , .…”

“…The belief operator Bel E (·) in the framework of [13] is given by Bel E (P) = {r ∈ L A | S |= r for all S ∈ U(P)}, where S |= r means that for each ground instance r ′ of r, either H(r ′ ) ∈ S, or L / ∈ S for some L ∈ B(r ′ ), or L ∈ S for some not L ∈ B(r ′ ).…”

“…For example, the formalisms of update programs [13,14], dynamic logic programs [2], revision programs [27,28], abductive theory updates [21], and updates through prioritized logic programs (PLPs) [34] fall into this class. (2) At a higher level, frameworks can be considered which allow for specifying an explicit update policy in some specification language, and which offer a greater flexibility in the handling of updates.…”

“…. , U n , into a (nonmonotonic) logic program P [2,34,21,13], to more general methods which use an update policy to specify, by means belief set Bel(s) of the agent, which comprises all formulas which the agent beliefs toshow that deciding whether two sequences P = (P 0 , . .…”