4 research outputs found
Semantics of Horn and disjunctive logic programs
AbstractVan Emden and Kowalski proposed a fixpoint semantics based on model-theory and an operational semantics based on proof-theory for Horn logic programs. They prove the equivalence of these semantics using fixpoint techniques. The main goal of this paper is to present a unified theory for the semantics of Horn and disjunctive logic programs. For this, we extend the fixpoint semantics and the operational or procedural semantics to the class of disjunctive logic programs and prove their equivalence using techniques similar to the ones used for Horn programs
Human Conditional Reasoning in Answer Set Programming
Given a conditional sentence "P=>Q" (if P then Q) and respective facts, four
different types of inferences are observed in human reasoning. Affirming the
antecedent (AA) (or modus ponens) reasons Q from P; affirming the consequent
(AC) reasons P from Q; denying the antecedent (DA) reasons -Q from -P; and
denying the consequent (DC) (or modus tollens) reasons -P from -Q. Among them,
AA and DC are logically valid, while AC and DA are logically invalid and often
called logical fallacies. Nevertheless, humans often perform AC or DA as
pragmatic inference in daily life. In this paper, we realize AC, DA and DC
inferences in answer set programming. Eight different types of completion are
introduced and their semantics are given by answer sets. We investigate formal
properties and characterize human reasoning tasks in cognitive psychology.
Those completions are also applied to commonsense reasoning in AI.Comment: 34 pages. Shorter version: in Proceedings of the 21st International
Workshop on Non-Monotonic Reasoning (NMR-2023
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Using Extended Logic Programs to Formalize Commonsense Reasoning
In this dissertation, we investigate how commonsense reasoning can be formalized by using extended logic programs. In this investigation, we first use extended logic programs to formalize inheritance hierarchies with exceptions by adopting McCarthy's simple abnormality formalism to express uncertain knowledge. In our representation, not only credulous reasoning can be performed but also the ambiguity-blocking inheritance and the ambiguity-propagating inheritance in skeptical reasoning are simulated. In response to the anomalous extension problem, we explore and discover that the intuition underlying commonsense reasoning is a kind of forward reasoning. The unidirectional nature of this reasoning is applied by many reformulations of the Yale shooting problem to exclude the undesired conclusion. We then identify defeasible conclusions in our representation based on the syntax of extended logic programs. A similar idea is also applied to other formalizations of commonsense reasoning to achieve such a purpose