42,514 research outputs found
FO(FD): Extending classical logic with rule-based fixpoint definitions
We introduce fixpoint definitions, a rule-based reformulation of fixpoint
constructs. The logic FO(FD), an extension of classical logic with fixpoint
definitions, is defined. We illustrate the relation between FO(FD) and FO(ID),
which is developed as an integration of two knowledge representation paradigms.
The satisfiability problem for FO(FD) is investigated by first reducing FO(FD)
to difference logic and then using solvers for difference logic. These
reductions are evaluated in the computation of models for FO(FD) theories
representing fairness conditions and we provide potential applications of
FO(FD).Comment: Presented at ICLP 2010. 16 pages, 1 figur
Synthesizing and executing plans in Knowledge and Action Bases
We study plan synthesis for a variant of Knowledge and Action Bases (KABs). KABs have been recently introduced as a rich, dynamic framework where states are full-fledged description logic (DL) knowledge bases (KBs) whose extensional part is manipulated by actions that can introduce new objects from an infinite domain. We show that, in general, plan existence over KABs is undecidable even under severe restrictions. We then focus on the class of state-bounded KABs, for which plan existence is decidable, and we provide sound and complete plan synthesis algorithms, through a novel combination of techniques based on standard planning, DL query answering, and finite-state abstractions. All results hold for any DL with decidable query answering. We finally show that for lightweight DLs, plan synthesis can be compiled into standard ADL planning. © 2016, CEUR-WS. All rights reserved
Rewritability in Monadic Disjunctive Datalog, MMSNP, and Expressive Description Logics
We study rewritability of monadic disjunctive Datalog programs, (the
complements of) MMSNP sentences, and ontology-mediated queries (OMQs) based on
expressive description logics of the ALC family and on conjunctive queries. We
show that rewritability into FO and into monadic Datalog (MDLog) are decidable,
and that rewritability into Datalog is decidable when the original query
satisfies a certain condition related to equality. We establish
2NExpTime-completeness for all studied problems except rewritability into MDLog
for which there remains a gap between 2NExpTime and 3ExpTime. We also analyze
the shape of rewritings, which in the MMSNP case correspond to obstructions,
and give a new construction of canonical Datalog programs that is more
elementary than existing ones and also applies to formulas with free variables
Plan Synthesis for Knowledge and Action Bases
We study plan synthesis for a variant of Knowledge and Action Bases (KABs), a rich, dynamic framework, where states are description logic (DL) knowledge bases (KBs) whose extensional part is manipulated by actions that possibly introduce new objects from an infinite domain. We show that plan existence over KABs is undecidable even under severe restrictions. We then focus on state-bounded KABs, a class for which plan existence is decidable, and provide sound and complete plan synthesis algorithms, which combine techniques based on standard planning, DL query answering, and finite-state abstraction. All results hold for any DL with decidable query answering. We finally show that for lightweight DLs, plan synthesis can be compiled into standard ADL planning
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