Assumption-free Semantics for Ordered Logic Programs: On the Relationship Between Well-founded and Stable Partial Models

1992 ◽  
Vol 2 (2) ◽  
pp. 133-172 ◽  
Author(s):  
E. LAENENS ◽  
D. VERMEIR
Keyword(s):  
Logic Programs ◽  
Partial Models ◽  
Ordered Logic ◽  
The Relationship

scholarly journals Stratified, Weak Stratified, and Three-Valued Semantics1

1990 ◽  
Vol 13 (1) ◽  
pp. 19-33
Author(s):  
Melvin Fitting ◽  
Marion Ben-Jacob
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Horn Clause ◽  
Logic Programs ◽  
The Family ◽  
Fixed Point Semantics ◽  
Truth Value ◽  
The Relationship ◽  
Classical Truth

We investigate the relationship between three-valued Kripke/Kleene semantics and stratified semantics for stratifiable logic programs. We first show these are compatible, in the sense that if the three-valued semantics assigns a classical truth value, the stratified approach will assign the same value. Next, the familiar fixed point semantics for pure Horn clause programs gives both smallest and biggest fixed points fundamental roles. We show how to extend this idea to the family of stratifiable logic programs, producing a semantics we call weak stratified. Finally, we show weak stratified semantics coincides exactly with the three-valued approach on stratifiable programs, though the three-valued version is generally applicable, and does not require stratification assumptions.

On the relationship between TMS and logic programs

1994 ◽  
Vol 9 (3) ◽  
pp. 245-251
Author(s):  
Xianchang Wang ◽  
Huowang Chen ◽  
Qinping Zhao
Keyword(s):  
Logic Programs ◽  
The Relationship

scholarly journals Extended ASP Tableaux and rule redundancy in normal logic programs

2008 ◽  
Vol 8 (5-6) ◽  
pp. 691-716 ◽  
Author(s):  
MATTI JÄRVISALO ◽  
EMILIA OIKARINEN
Keyword(s):  
Answer Set Programming ◽  
Proof System ◽  
Logic Programs ◽  
Interesting Insight ◽  
Extension Rule ◽  
Normal Logic ◽  
Relationship Of ◽  
The Relationship ◽  
Resolution Proof ◽  
Answer Set

AbstractWe introduce an extended tableau calculus for answer set programming (ASP). The proof system is based on the ASP tableaux defined in the work by Gebser and Schaub (Tableau calculi for answer set programming. In Proceedings of the 22nd International Conference on Logic Programming (ICLP 2006), S. Etalle and M. Truszczynski, Eds. Lecture Notes in Computer Science, vol. 4079. Springer, 11–25) with an added extension rule. We investigate the power of Extended ASP Tableaux both theoretically and empirically. We study the relationship of Extended ASP Tableaux with the Extended Resolution proof system defined by Tseitin for sets of clauses, and separate Extended ASP Tableaux from ASP Tableaux by giving a polynomial-length proof for a family of normal logic programs {Φn} for which ASP Tableaux has exponential-length minimal proofs with respect to n. Additionally, Extended ASP Tableaux imply interesting insight into the effect of program simplification on the lengths of proofs in ASP. Closely related to Extended ASP Tableaux, we empirically investigate the effect of redundant rules on the efficiency of ASP solving.

scholarly journals A framework for compiling preferences in logic programs

2003 ◽  
Vol 3 (2) ◽  
pp. 129-187 ◽  
Author(s):  
JAMES P. DELGRANDE ◽  
TORSTEN SCHAUB ◽  
HANS TOMPITS
Keyword(s):  
Logic Program ◽  
Logic Programs ◽  
Wide Range ◽  
Dynamic Case ◽  
General Preference ◽  
Reasoning With Preferences ◽  
Answer Set Semantics ◽  
Ordered Logic ◽  
Answer Sets ◽  
General Dynamic

We introduce a methodology and framework for expressing general preference information in logic programming under the answer set semantics. An ordered logic program is an extended logic program in which rules are named by unique terms, and in which preferences among rules are given by a set of atoms of form s [pr ] t where s and t are names. An ordered logic program is transformed into a second, regular, extended logic program wherein the preferences are respected, in that the answer sets obtained in the transformed program correspond with the preferred answer sets of the original program. Our approach allows the specification of dynamic orderings, in which preferences can appear arbitrarily within a program. Static orderings (in which preferences are external to a logic program) are a trivial restriction of the general dynamic case. First, we develop a specific approach to reasoning with preferences, wherein the preference ordering specifies the order in which rules are to be applied. We then demonstrate the wide range of applicability of our framework by showing how other approaches, among them that of Brewka and Eiter, can be captured within our framework. Since the result of each of these transformations is an extended logic program, we can make use of existing implementations, such as dlv and smodels. To this end, we have developed a publicly available compiler as a front-end for these programming systems.

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