Since Logic Programming (LP) and Description Logics (DLs) are based on different assumptions (the closed and the open world assumption, respectively), combining them provides higher expressiveness in applications that require both assumptions. Several proposals have been made to combine LP and DLs. An especially successful line of research is the one based on Lifschitz’s logic of Minimal Knowledge with Negation as Failure (MKNF). Motik and Rosati introduced Hybrid knowledge bases (KBs), composed of LP rules and DL axioms, gave them an MKNF semantics and studied their complexity. Knorr et al. proposed a well-founded semantics for Hybrid KBs where the LP clause heads are non-disjunctive, which keeps querying polynomial (provided the underlying DL is polynomial) even when the LP portion is non-stratified. In this paper, we propose Probabilistic Hybrid Knowledge Bases (PHKBs), where the atom in the head of LP clauses and each DL axiom is annotated with a probability value. PHKBs are given a distribution semantics by defining a probability distribution over deterministic Hybrid KBs. The probability of a query being true is the sum of the probabilities of the deterministic KBs that entail the query. Both epistemic and statistical probability can be addressed, thanks to the integration of probabilistic LP and DLs.

Probabilistic Hybrid Knowledge Bases under the Distribution Semantics

ALBERTI, Marco;LAMMA, Evelina;RIGUZZI, Fabrizio
;
ZESE, Riccardo
2016

Abstract

Since Logic Programming (LP) and Description Logics (DLs) are based on different assumptions (the closed and the open world assumption, respectively), combining them provides higher expressiveness in applications that require both assumptions. Several proposals have been made to combine LP and DLs. An especially successful line of research is the one based on Lifschitz’s logic of Minimal Knowledge with Negation as Failure (MKNF). Motik and Rosati introduced Hybrid knowledge bases (KBs), composed of LP rules and DL axioms, gave them an MKNF semantics and studied their complexity. Knorr et al. proposed a well-founded semantics for Hybrid KBs where the LP clause heads are non-disjunctive, which keeps querying polynomial (provided the underlying DL is polynomial) even when the LP portion is non-stratified. In this paper, we propose Probabilistic Hybrid Knowledge Bases (PHKBs), where the atom in the head of LP clauses and each DL axiom is annotated with a probability value. PHKBs are given a distribution semantics by defining a probability distribution over deterministic Hybrid KBs. The probability of a query being true is the sum of the probabilities of the deterministic KBs that entail the query. Both epistemic and statistical probability can be addressed, thanks to the integration of probabilistic LP and DLs.
2016
978-3-319-49129-5
978-3-319-49130-1
Hybrid knowledge bases, MKNF, Distribution semantics
File in questo prodotto:
File Dimensione Formato  
main.pdf

accesso aperto

Tipologia: Post-print
Licenza: PUBBLICO - Pubblico con Copyright
Dimensione 292.77 kB
Formato Adobe PDF
292.77 kB Adobe PDF Visualizza/Apri
full text phkb.pdf

solo gestori archivio

Descrizione: articolo principale
Tipologia: Full text (versione editoriale)
Licenza: NON PUBBLICO - Accesso privato/ristretto
Dimensione 190.97 kB
Formato Adobe PDF
190.97 kB Adobe PDF   Visualizza/Apri   Richiedi una copia

I documenti in SFERA sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11392/2350957
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 2
  • ???jsp.display-item.citation.isi??? 3
social impact