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Related papers: Rational Closure in SHIQ

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In this work we attempt to generalize our result in [6] [7] for real rings (not just von Neumann regular real rings). In other words we attempt to characterize and construct real closure * of commutative unitary rings that are real. We also…

Rings and Algebras · Mathematics 2009-12-07 Jose Capco

In their seminal paper Artemov and Protopopescu provide Hilbert formal systems, Brower-Heyting-Kolmogorov and Kripke semantics for the logics of intuitionistic belief and knowledge. Subsequently Krupski has proved that the logic of…

Logic · Mathematics 2021-03-08 Guido Fiorino

Fitch-style modal deduction, in which modalities are eliminated by opening a subordinate proof, and introduced by shutting one, were investigated in the 1990s as a basis for lambda calculi. We show that such calculi have good computational…

Logic in Computer Science · Computer Science 2018-01-22 Ranald Clouston

We give the first ExpTime (complexity-optimal) tableau decision procedure for checking satisfiability of a knowledge base in the description logic SHIQ when numbers are coded in unary. Our procedure is based on global state caching and…

Logic in Computer Science · Computer Science 2014-01-03 Linh Anh Nguyen

This paper introduces two sequent calculi for intuitionistic strong L\"ob logic ${\sf iSL}_\Box$: a terminating sequent calculus ${\sf G4iSL}_\Box$ based on the terminating sequent calculus ${\sf G4ip}$ for intuitionistic propositional…

Logic · Mathematics 2023-03-07 Iris van der Giessen , Rosalie Iemhoff

In 1997 Timothy J. Surendonk proved via algebraic semantics that all modal logics without iterative axioms are canonical and so strongly complete. In this paper, we continue the work done by Surendonk in this field. We use neighborhood…

Logic · Mathematics 2023-05-16 Kirill Kopnev

Motivated by the quest for a logic for PTIME and recent insights that the descriptive complexity of problems from linear algebra is a crucial aspect of this problem, we study the solvability of linear equation systems over finite groups and…

Logic in Computer Science · Computer Science 2015-07-01 Anuj Dawar , Eryk Kopczynski , Bjarki Holm , Erich Grädel , Wied Pakusa

We study bisimulations for useful description logics. The simplest among the considered logics is $\mathcal{ALC}_{reg}$ (a variant of PDL). The others extend that logic with inverse roles, nominals, quantified number restrictions, the…

Logic in Computer Science · Computer Science 2015-02-20 Ali Rezaei Divroodi , Linh Anh Nguyen

In this paper we introduce an enclosure of the numerical range of a class of rational operator functions. In contrast to the numerical range the presented enclosure can be computed exactly in the infinite dimensional case as well as in the…

Functional Analysis · Mathematics 2017-04-25 Christian Engström , Axel Torshage

We give the first ExpTime (complexity-optimal) tableau decision procedure for checking satisfiability of a knowledge base in the description logic SHOQ, which extends the basic description logic ALC with transitive roles, hierarchies of…

Logic in Computer Science · Computer Science 2014-07-22 Linh Anh Nguyen , Joanna Golińska-Pilarek

The inexpressive Description Logic (DL) $\mathcal{FL}_0$, which has conjunction and value restriction as its only concept constructors, had fallen into disrepute when it turned out that reasoning in $\mathcal{FL}_0$ w.r.t. general TBoxes is…

Artificial Intelligence · Computer Science 2021-07-28 Franz Baader , Patrick Koopmann , Friedrich Michel , Anni-Yasmin Turhan , Benjamin Zarrieß

This paper presents a method for the evolution of SHI ABoxes which is based on a compilation technique of the knowledge base. For this the ABox is regarded as an interpretation of the TBox which is close to a model. It is shown, that the…

Logic in Computer Science · Computer Science 2014-05-07 Ulrich Furbach , Claudia Schon

With recent advances in natural language processing, rationalization becomes an essential self-explaining diagram to disentangle the black box by selecting a subset of input texts to account for the major variation in prediction. Yet,…

Machine Learning · Computer Science 2023-09-12 Wenbo Zhang , Tong Wu , Yunlong Wang , Yong Cai , Hengrui Cai

We propose new sequent calculus systems for orthologic (also known as minimal quantum logic) which satisfy the cut elimination property. The first one is a simple system relying on the involutive status of negation. The second one…

Logic in Computer Science · Computer Science 2023-06-22 Olivier Laurent

A natural kind of compactification of the virtual moduli spaces of rational functions of one complex variable is given. To describe the boundary points geometrically, the authors introduce the concept of rational functions with nodes,…

Complex Variables · Mathematics 2016-02-16 Masayo Fujimura , Masahiko Taniguchi

Definite descriptions, such as 'the General Chair of KR 2024', are a semantically transparent device for object identification in knowledge representation. In first-order modal logic, definite descriptions have been widely investigated for…

Logic in Computer Science · Computer Science 2024-09-12 Alessandro Artale , Roman Kontchakov , Andrea Mazzullo , Frank Wolter

We give effective bounds for the set quasi-integral points in orbits of non-isotrivial rational maps over function fields under some conditions, generalizing previous work of Hsia and Silverman (2011) for orbits over function fields of…

Number Theory · Mathematics 2020-12-04 Jorge Mello

We give an automata-theoretic description of the algebraic closure of the rational function field F_q(t) over a finite field, generalizing a result of Christol. The description takes place within the Hahn-Mal'cev-Neumann field of…

Commutative Algebra · Mathematics 2007-05-23 Kiran S. Kedlaya

We define a closure operation for ideals in a commutative ring which has all the good properties of solid closure (at least in the case of equal characteristic) but such that also every ideal in a regular ring is closed. This gives in…

Commutative Algebra · Mathematics 2007-05-23 Holger Brenner

We study the topological models of a logic of knowledge for topological reasoning, introduced by Larry Moss and Rohit Parikh. Among our results is a solution of a conjecture by the formentioned authors, finite satisfiability property and…

Logic in Computer Science · Computer Science 2007-05-23 Konstantinos Georgatos