Decision Procedures for Guarded Logics

11/09/2019
by   Kevin Kappelmann, et al.
0

An important class of decidable first-order logic fragments are those satisfying a guardedness condition, such as the guarded fragment (GF). Usually, decidability for these logics is closely linked to the tree-like model property - the fact that satisfying models can be taken to have tree-like form. Decision procedures for the guarded fragment based on the tree-like model property are difficult to implement. An alternative approach, based on restricting first-order resolution, has been proposed, and this shows more promise from the point of view of implementation. In this work, we connect the tree-like model property of the guarded fragment with the resolution-based approach. We derive efficient resolution-based rewriting algorithms that solve the Quantifier-Free Query Answering Problem under Guarded Tuple Generating Dependencies (GTGDs) and Disjunctive Guarded Tuple Generating Dependencies (DisGTGDs). The Query Answering Problem for these classes subsumes many cases of GF satisfiability. Our algorithms, in addition to making the connection to the tree-like model property clear, give a natural account of the selection and ordering strategies used by resolution procedures for the guarded fragment. We also believe that our rewriting algorithm for the special case of GTGDs may prove itself valuable in practice as it does not require any Skolemisation step and its theoretical runtime outperforms those of known GF resolution procedures in case of fixed dependencies. Moreover, we show a novel normalisation procedure for the widely used chase procedure in case of (disjunctive) GTGDs, which could be useful for future studies.

READ FULL TEXT

page 1

page 2

page 3

page 4

research
08/10/2022

Saturation-based Boolean conjunctive query answering and rewriting for the guarded quantification fragments

Answering Boolean conjunctive query over logical constraints is an essen...
research
08/09/2018

Finite Query Answering in Expressive Description Logics with Transitive Roles

We study the problem of finite ontology mediated query answering (FOMQA)...
research
02/10/2023

Constraint Automata on Infinite Data Trees: From CTL(Z)/CTL*(Z) To Decision Procedures

We introduce the class of tree constraint automata with data values in Z...
research
03/13/2023

A Framework for Combining Entity Resolution and Query Answering in Knowledge Bases

We propose a new framework for combining entity resolution and query ans...
research
12/15/2018

Decidable fragments of first-order modal logics with counting quantifiers over varying domains

This paper explores the computational complexity of various natural one-...
research
12/16/2022

Rewriting the Infinite Chase

Guarded tuple-generating dependencies (GTGDs) are a natural extension of...
research
02/27/2013

Modus Ponens Generating Function in the Class of ^-valuations of Plausibility

We discuss the problem of construction of inference procedures which can...

Please sign up or login with your details

Forgot password? Click here to reset