Nonmonotonic logic and temporal projection
Artificial Intelligence
Journal of Logic Programming
The anomalous extension problem in default reasoning
Artificial Intelligence
Foundations of deductive databases and logic programming
Towards a theory of declarative knowledge
Foundations of deductive databases and logic programming
Negation as failure using tight derivations for general logic programs
Foundations of deductive databases and logic programming
On the declarative semantics of logic programs with negation
Foundations of deductive databases and logic programming
The alternating fixpoint of logic programs with negation
PODS '89 Proceedings of the eighth ACM SIGACT-SIGMOD-SIGART symposium on Principles of database systems
Every logic program has a natural stratification and an iterated least fixed point model
PODS '89 Proceedings of the eighth ACM SIGACT-SIGMOD-SIGART symposium on Principles of database systems
Logic programming as constructivism: a formalization and its application to databases
PODS '89 Proceedings of the eighth ACM SIGACT-SIGMOD-SIGART symposium on Principles of database systems
Three-valued formalizations of non-monotonic reasoning and logic programming
Proceedings of the first international conference on Principles of knowledge representation and reasoning
Unfounded sets and well-founded semantics for general logic programs
Proceedings of the seventh ACM SIGACT-SIGMOD-SIGART symposium on Principles of database systems
The valid model semantics for logic programs
PODS '92 Proceedings of the eleventh ACM SIGACT-SIGMOD-SIGART symposium on Principles of database systems
A three-valued semantics for deductive databases and logic programs
Journal of Computer and System Sciences
On the partial semantics for disjunctive deductive databases
Annals of Mathematics and Artificial Intelligence
Alternating Fixpoint Theory for Logic Programs with Priority
CL '00 Proceedings of the First International Conference on Computational Logic
Rules and logic programming for the web
RW'11 Proceedings of the 7th international conference on Reasoning web: semantic technologies for the web of data
Analysing and extending well-founded and partial stable semantics using partial equilibrium logic
ICLP'06 Proceedings of the 22nd international conference on Logic Programming
A Classification Theory Of Semantics Of Normal Logic Programs: I. Strong Properties
Fundamenta Informaticae
A Classification Theory Of Semantics Of Normal Logic Programs: Ii. Weak Properties
Fundamenta Informaticae
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The central issue of this paper concerns the truth value undefined in Przymusinsi's 3-valued formalization of nonmonotonic reasoning and logic programming. We argue that this formalization can lead to the problem of unintended semantics and loss of disjunctive information. We modify the formalization by proposing two general principles for logic program semantics: justifiability and minimal undefinedness. The former is shown to be a general property for almost all logic program semantics, and the latter requires the use of the undefined only when it is necessary. We show that there are three types of information embedded in the undefined: the disjunctive, the factoring, and the “difficult-to-be-assigned”. In the modified formalization, the first two can be successfully identified and branched into multiple models. This leaves only the “difficult-to-be-assigned” as the undefined. It is shown that the truth value undefined is needed only for a very special type of programs whose practicality is yet to be evidenced.