621 research outputs found
Stratified least fixpoint logic
Stratified least fixpoint logic, or SLFP, characterizes the expressibility of stratified logic programs and, in a different formulation, has been used as a logic of imperative programs. These two formulations of SLFP are proved to be equivalent. A complete sequent calculus with one infinitary rule is given for SLFP. It is argued that SLFP is the most appropriate assertion language for program verification. In particular, it is shown that traditional approaches using first-order logic as an assertion language only restrict to interpretations where first-order logic has the same expressibility as SLFP.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/31383/1/0000296.pd
Stratified least fixpoint logic
Stratified least fixpoint logic or SLFP characterizes the expressibility of stratified logic programs and in a different formulation has been used as a logic of imperative programs. These two formulations of SLFP are proved to be equivalent and a complete sequent calculus for SLFP is presented. It is argued that SLFP is the most appropriate assertion language for program verification. In particular, it is shown that traditional approaches using first-order logic as an assertion language only restrict to interpretations where first-order logic has the same expressibility as SLFP
Logic Programming as Constructivism
The features of logic programming that
seem unconventional from the viewpoint of classical logic
can be explained in terms of constructivistic logic. We
motivate and propose a constructivistic proof theory of
non-Horn logic programming. Then, we apply this formalization
for establishing results of practical interest.
First, we show that 'stratification can be motivated in a
simple and intuitive way. Relying on similar motivations,
we introduce the larger classes of 'loosely stratified' and
'constructively consistent' programs. Second, we give a
formal basis for introducing quantifiers into queries and
logic programs by defining 'constructively domain
independent* formulas. Third, we extend the Generalized
Magic Sets procedure to loosely stratified and constructively
consistent programs, by relying on a 'conditional
fixpoini procedure
Ultimate approximations in nonmonotonic knowledge representation systems
We study fixpoints of operators on lattices. To this end we introduce the
notion of an approximation of an operator. We order approximations by means of
a precision ordering. We show that each lattice operator O has a unique most
precise or ultimate approximation. We demonstrate that fixpoints of this
ultimate approximation provide useful insights into fixpoints of the operator
O.
We apply our theory to logic programming and introduce the ultimate
Kripke-Kleene, well-founded and stable semantics. We show that the ultimate
Kripke-Kleene and well-founded semantics are more precise then their standard
counterparts We argue that ultimate semantics for logic programming have
attractive epistemological properties and that, while in general they are
computationally more complex than the standard semantics, for many classes of
theories, their complexity is no worse.Comment: This paper was published in Principles of Knowledge Representation
and Reasoning, Proceedings of the Eighth International Conference (KR2002
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