Download:
by Robert F. St Ärk, Universität Bern
http://www.inf.ethz.ch/~staerk/pdf/cut.pdf
Add To MetaCart
Abstract:
What is the semantics of Negation-as-Failure in logic programming? We try to answer this question by proof-theoretic methods. A rule based sequent calculus is used in which a sequent is provable if, and only if, it is true in all three-valued models of the completion of a logic program. The main theorem is that proofs in the sequent calculus can be transformed into SLDNF-computations if, and only if, a program has the cut-property. A fragment of the sequent calculus leads to a sound and complete semantics for SLDNFresolution with substitutions. It turns out that this version of SLDNF-resolution is sound and complete with respect to three-valued possible world models of the completion for arbitrary logic programs and arbitrary goals. Since we are dealing with possibly nonterminating computations and constructive proofs, three-valued possible world models seem to be an appropriate semantics. Keywords: Logic programming; proof theory; Negation-as-Failure; SLDNF-resolution; three-valued logic.
Citations
|
1654
|
Foundations of Logic Programming
– Lloyd
- 1984
|
|
1126
|
The Stable Model Semantics for Logic Programming
– Gelfond, Lifschitz
- 1988
|
|
787
|
Negation as Failure
– Clark
- 1978
|
|
557
|
Towards a theory of Declarative Knowledge
– Apt, Blair, et al.
- 1988
|
|
496
|
An Introduction to Metamathematics
– Kleene
- 1950
|
|
387
|
Logic programming
– Apt
- 1990
|
|
332
|
Uniform proofs as a foundation for logic programming
– Miller, Nadathur, et al.
- 1991
|
|
325
|
Bilattices and the semantics of logic programming
– Fitting
- 1991
|
|
263
|
A Logic Programming Language with Lambda-Abstraction, Function Variables, and Simple Unification
– Miller
- 1991
|
|
214
|
Negation in logic programming
– Kunen
- 1987
|
|
213
|
Unification Revisited
– Lassez, Maher, et al.
- 1988
|
|
94
|
Signed data dependencies in logic programs
– Kunen
- 1989
|
|
59
|
Higher-order horn clauses
– Nadathur, Miller
- 1990
|
|
54
|
A Proof-Theoretical Approach to Logic Programming
– Halln��s, Schroeder-Heister
- 1991
|
|
44
|
Weakly perfect model semantics for logic programs
– Przymusinska, Przymusinski
- 1988
|
|
32
|
A Completeness Theorem for SLDNF-Resolution
– Cavedon, Lloyd
- 1989
|
|
24
|
Proof Theory and Logical Complexity
– Girard
- 1987
|
|
20
|
A linear semantics for allowed logic programs
– Cerrito
- 1990
|
|
18
|
Completeness of the Negation as Failure Rule
– Jaffar, Lassez, et al.
- 1983
|
|
17
|
Cut-elimination in logics with definitional reflection
– Schroeder-Heister
- 1992
|
|
12
|
Finitary Partial Inductive Definitions and General Logic
– Eriksson
- 1993
|
|
11
|
The defining power of stratified and hierarchical logic programs
– Jäger, Stärk
- 1993
|
|
7
|
A fixpoint theorem in linear logic. A message posted on the linear@cs.stanford.edu mailing listing, http://www.csl.sri.com/linear/ mailing-list-traffic/www/07/mail3.html
– Girard
- 1992
|
|
3
|
Some proof-theoretic aspects of logic programming
– Jäger
- 1993
|
