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Event Entry

What and Who

On a Notion of Abduction and Relevance for First-Order Logic Clause Sets

Fajar Haifani
Max-Planck-Institut für Informatik - RG 1
AG 1, AG 2, AG 3, INET, AG 4, AG 5, D6, SWS, RG1, MMCI  
Public Audience

Date, Time and Location

Thursday, 9 March 2023
90 Minutes
E1 4


I propose techniques to help explain entailment and non-entailment in first-order logic. For entailment, I classify clauses necessary for any possible deduction (syntactically relevant), usable for some deduction (syntactically semi-relevant), or unusable (syntactically irrelevant) along with a semantic characterization via conflict literals (contradictory simple facts). This offers a novel insight beyond the existing notion of minimal unsatisfiable set. The need to test if a clause is syntactically semi-relevant leads to a generalization of the completeness result of a well-known resolution strategy: resolution with the set-of-support (SOS) strategy is refutationally complete on a
clause set N and SOS M if and only if there is a resolution refutation from N ∪ M using a clause in M. For non-entailment, abductive reasoning helps find extensions of a knowledge base to obtain an entailment of some missing consequence. I focus on EL TBox abduction that is lightweight but prevalent in practice. The solution space can be huge so, to help sort the chaff from the grain, I introduce
connection-minimality, a criterion such that accepted hypotheses always immediately relate the observation to the given axioms. I show that such hypotheses are computable using prime implicate-based abduction in first-order logic. I evaluate this notion on ontologies from the medical domain using an implementation with SPASS as a prime implicate generation engine.


Jennifer Müller
+49 681 9325 2900
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Jennifer Müller, 02/27/2023 11:46 -- Created document.