11 research outputs found
Even shorter proofs without new variables
Proof formats for SAT solvers have diversified over the last decade, enabling
new features such as extended resolution-like capabilities, very general
extension-free rules, inclusion of proof hints, and pseudo-boolean reasoning.
Interference-based methods have been proven effective, and some theoretical
work has been undertaken to better explain their limits and semantics. In this
work, we combine the subsumption redundancy notion from (Buss, Thapen 2019) and
the overwrite logic framework from (Rebola-Pardo, Suda 2018). Natural
generalizations then become apparent, enabling even shorter proofs of the
pigeonhole principle (compared to those from (Heule, Kiesl, Biere 2017)) and
smaller unsatisfiable core generation.Comment: 21 page
Defeasible Reasoning in SROEL: from Rational Entailment to Rational Closure
In this work we study a rational extension of the low complexity
description logic SROEL, which underlies the OWL EL ontology language. The
extension involves a typicality operator T, whose semantics is based on Lehmann
and Magidor's ranked models and allows for the definition of defeasible
inclusions. We consider both rational entailment and minimal entailment. We
show that deciding instance checking under minimal entailment is in general
-hard, while, under rational entailment, instance checking can be
computed in polynomial time. We develop a Datalog calculus for instance
checking under rational entailment and exploit it, with stratified negation,
for computing the rational closure of simple KBs in polynomial time.Comment: Accepted for publication on Fundamenta Informatica
Axiomatizing hybrid xpath with data
In this paper we introduce sound and strongly complete axiomatizations for XPath with data constraints extended with hybrid operators. First, we present HXPath=, a multi-modal version of XPath with data, extended with nominals and the hybrid operator @. Then, we introduce an axiomatic system for HXPath=, and we prove it is strongly complete with respect to the class of abstract data models, i.e., data models in which data values are abstracted as equivalence relations. We prove a general completeness result similar to the one presented in, e.g., [BtC06], that ensures that certain extensions of the axiomatic system we introduce are also complete. The axiomatic systems that can be obtained in this way cover a large family of hybrid XPath languages over different classes of frames, for which we present concrete examples. In addition, we investigate axiomatizations over the class of tree models, structures widely used in practice. We show that a strongly complete, finitary, first-order axiomatization of hybrid XPath over trees does not exist, and we propose two alternatives to deal with this issue. We finally introduce filtrations to investigate the status of decidability of the satisfiability problem for these languages.Fil: Areces, Carlos Eduardo. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física. Sección Ciencias de la Computación; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba; ArgentinaFil: Fervari, Raul Alberto. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física. Sección Ciencias de la Computación; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba; Argentin
Axiomatizing Hybrid XPath with Data
In this paper we introduce sound and strongly complete axiomatizations for
XPath with data constraints extended with hybrid operators. First, we present
HXPath=, a multi-modal version of XPath with data, extended with nominals and
the hybrid operator @. Then, we introduce an axiomatic system for HXPath=, and
we prove it is strongly complete with respect to the class of abstract data
models, i.e., data models in which data values are abstracted as equivalence
relations. We prove a general completeness result similar to the one presented
in, e.g., [BtC06], that ensures that certain extensions of the axiomatic system
we introduce are also complete. The axiomatic systems that can be obtained in
this way cover a large family of hybrid XPath languages over different classes
of frames, for which we present concrete examples. In addition, we investigate
axiomatizations over the class of tree models, structures widely used in
practice. We show that a strongly complete, finitary, first-order
axiomatization of hybrid XPath over trees does not exist, and we propose two
alternatives to deal with this issue. We finally introduce filtrations to
investigate the status of decidability of the satisfiability problem for these
languages
How we designed winning algorithms for abstract argumentation and which insight we attained
In this paper we illustrate the design choices that led to the development of ArgSemSAT, the winner of the preferred semantics track at the 2017 International Competition on Computational Models of Arguments (ICCMA 2017), a biennial contest on problems associated to the Dung’s model of abstract argumentation frameworks, widely recognised as a fundamental reference in computational argumentation. The algorithms of ArgSemSAT are based on multiple calls to a SAT solver to compute complete labellings, and on encoding constraints to drive the search towards the solution of decision and enumeration problems. In this paper we focus on preferred semantics (and incidentally stable as well), one of the most popular and complex semantics for identifying acceptable arguments. We discuss our design methodology that includes a systematic exploration and empirical evaluation of labelling encodings, algorithmic variations and SAT solver choices. In designing the successful ArgSemSAT, we discover that: (1) there is a labelling encoding that appears to be universally better than other, logically equivalent ones; (2) composition of different techniques such as AllSAT and enumerating stable extensions when searching for preferred semantics brings advantages; (3) injecting domain specific knowledge in the algorithm design can lead to significant improvements