82 research outputs found
Multiple Conclusion Rules in Logics with the Disjunction Property
We prove that for the intermediate logics with the disjunction property any
basis of admissible rules can be reduced to a basis of admissible m-rules
(multiple-conclusion rules), and every basis of admissible m-rules can be
reduced to a basis of admissible rules. These results can be generalized to a
broad class of logics including positive logic and its extensions, Johansson
logic, normal extensions of S4, n-transitive logics and intuitionistic modal
logics
From Display to Labelled Proofs for Tense Logics
We introduce an effective translation from proofs in the display calculus to proofs in the labelled calculus in the context of tense logics. We identify the labelled calculus proofs in the image of this translation as those built from labelled sequents whose underlying directed graph possesses certain properties. For the basic normal tense logic Kt, the image is shown to be the set of all proofs in the labelled calculus G3Kt
An introduction to description logics and query rewriting
This chapter gives an overview of the description logics underlying the OWL 2 Web Ontology Language and its three tractable profiles, OWL 2 RL, OWL 2 EL and OWL 2 QL. We consider the syntax and semantics of these description logics as well as main reasoning tasks and their computational complexity. We also discuss the semantical foundations for fist-order and datalog rewritings of conjunctive queries over knowledge bases given in the OWL2 profiles, and outline the architecture of the ontology-based data access system Ontop
Changing a semantics: opportunism or courage?
The generalized models for higher-order logics introduced by Leon Henkin, and
their multiple offspring over the years, have become a standard tool in many
areas of logic. Even so, discussion has persisted about their technical status,
and perhaps even their conceptual legitimacy. This paper gives a systematic
view of generalized model techniques, discusses what they mean in mathematical
and philosophical terms, and presents a few technical themes and results about
their role in algebraic representation, calibrating provability, lowering
complexity, understanding fixed-point logics, and achieving set-theoretic
absoluteness. We also show how thinking about Henkin's approach to semantics of
logical systems in this generality can yield new results, dispelling the
impression of adhocness. This paper is dedicated to Leon Henkin, a deep
logician who has changed the way we all work, while also being an always open,
modest, and encouraging colleague and friend.Comment: 27 pages. To appear in: The life and work of Leon Henkin: Essays on
his contributions (Studies in Universal Logic) eds: Manzano, M., Sain, I. and
Alonso, E., 201
Admissible Bases Via Stable Canonical Rules
We establish the dichotomy property for stable canonical multi-conclusion rules for IPC, K4, and S4. This yields an alternative proof of existence of explicit bases of admissible rules for these logics
Quantified epistemic logics for reasoning about knowledge in multi-agent systems
AbstractWe introduce quantified interpreted systems, a semantics to reason about knowledge in multi-agent systems in a first-order setting. Quantified interpreted systems may be used to interpret a variety of first-order modal epistemic languages with global and local terms, quantifiers, and individual and distributed knowledge operators for the agents in the system. We define first-order modal axiomatisations for different settings, and show that they are sound and complete with respect to the corresponding semantical classes.The expressibility potential of the formalism is explored by analysing two MAS scenarios: an infinite version of the muddy children problem, a typical epistemic puzzle, and a version of the battlefield game. Furthermore, we apply the theoretical results here presented to the analysis of message passing systems [R. Fagin, J. Halpern, Y. Moses, M. Vardi, Reasoning about Knowledge, MIT Press, 1995; L. Lamport, Time, clocks, and the ordering of events in a distributed system, Communication of the ACM 21 (7) (1978) 558–565], and compare the results obtained to their propositional counterparts. By doing so we find that key known meta-theorems of the propositional case can be expressed as validities on the corresponding class of quantified interpreted systems
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