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by Thomas Lukasiewicz
In Proceedings of the Annual Conference of the European Association for Computer Science Logic, 1998, volume 1584 of LNCS
http://www.kr.tuwien.ac.at/staff/lukasiew/csl98.ps.gz
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Abstract:
Abstract. We present n-valued first-order logics with a purely probabilistic semantics. We then introduce a new probabilistic semantics of n-valued first-order logics that lies between the purely probabilistic semantics and the truth-functional semantics of the n-valued / Lukasiewicz logics / Ln. Within this semantics, closed formulas of classical first-order logics that are logically equivalent in the classical sense also have the same truth value under all n-valued interpretations. Moreover, this semantics is shown to have interesting computational properties. More precisely, n-valued logical consequence in disjunctive logic programs with n-valued disjunctive facts can be reduced to classical logical consequence in n \Gamma 1 layers of classical disjunctive logic programs. Moreover, we show that n-valued logic programs have a model and a fixpoint semantics that are very similar to those of classical logic programs. Finally, we show that some important deduction problems in n-valued logic programs have the same computational complexity like their classical counterparts. 1
Citations
|
1654
|
Foundations of Logic Programming
– Lloyd
- 1984
|
|
1486
|
Fuzzy sets
– Zadeh
- 1965
|
|
387
|
Logic programming
– Apt
- 1990
|
|
325
|
Bilattices and the semantics of logic programming
– Fitting
- 1991
|
|
314
|
Probabilistic logic
– Nilsson
|
|
201
|
An analysis of first-order logics of probability
– Halpern
- 1990
|
|
166
|
Complexity and Expressive Power of Logic Programming
– Dantsin, Eiter, et al.
- 2001
|
|
166
|
Temporal Logic
– Rescher, Urquhart
- 1971
|
|
159
|
A logic for reasoning about probabilities
– Fagin, Halpern, et al.
- 1990
|
|
145
|
Logical Foundations of Probability
– Carnap
- 1950
|
|
139
|
Theory of Generalized Annotated Logic Programming and its Applications
– Kifer, Subrahmanian
- 1992
|
|
96
|
Amalgamating Knowledge Bases
– Subrahmanian
- 1994
|
|
92
|
Probabilistic Logic Programming
– Ng, Subrahmanian
- 1992
|
|
90
|
From statistical knowledge bases to degrees of belief
– Bacchus, Grove, et al.
- 1996
|
|
74
|
Quantitative Deduction and its Fixpoint Theory
– Emden
- 1986
|
|
61
|
Paraconsistent logic programming
– Blair, Subrahmanian
- 1989
|
|
58
|
Hybrid probabilistic programs
– Dekhtyar, Subrahmanian
- 1997
|
|
50
|
A Semantical Framework for Supporting Subjective and Conditional Probabilities in Deductive Databases
– Ng, Subrahmanian
- 1993
|
|
46
|
Stable Semantics for Probabilistic Deductive Databases
– Ng, Subrahmanian
- 1995
|
|
41
|
Probabilistic Deductive Databases
– Lakshmanan, Sadri
- 1994
|
|
40
|
Probabilistic deduction with conditional constraints over basic events
– Lukasiewicz
- 1999
|
|
34
|
Three-Valued Non-Monotonic Formalisms and Semantics of Logic Programs
– Przymusinski
- 1991
|
|
28
|
de Finetti Theory of Probability
– unknown authors
- 1974
|
|
28
|
Probabilistic logic programming
– Lukasiewicz
- 1998
|
|
20
|
Many-valued modal logics II
– Fitting
- 1992
|
|
19
|
Exploiting data dependencies in many-valued logics
– Hahnle
- 1996
|
|
17
|
Logic programming with signs and annotations
– Lu
- 1996
|
|
15
|
Query processing in annotated logic programming: theory and implementation
– Leach, Lu
- 1996
|
|
13
|
Many-valued Logics
– Rosser, Turquette
- 1952
|
|
12
|
Partial models and logic programming
– Fitting
- 1986
|
|
10
|
Semantics, consistency, and query processing of empirical deductive databases
– Ng
- 1997
|
|
7
|
Optimal fixedpoints of logic programs
– Lassez, Maher
- 1985
|
|
5
|
Efficient interpretation of propositional multi-valued logic programs
– Escalada-Imaz, Many`a
- 1995
|
|
5
|
Magic inference rules for probabilistic deduction under taxonomic knowledge
– Lukasiewicz
- 1998
|
|
4
|
Programming in three-valued logic
– Delahaye, Thibau
- 1991
|
