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Approximations of Modal Logic K

Guilherme de Souza Rabello, Marcelo Finger
2006 Electronical Notes in Theoretical Computer Science  
Inspired by the recent work on approximating classical logic, we present a procedure that approximates the modal logic K by determining a maximum limit of introspection.  ...  This procedure has a clear semantics and a natural proof theory in the context of Massacci's modal Single Step Tableaux (SST).  ...  Massacci, in [7] , has developed a different method of approximating modal logics.  ... 
doi:10.1016/j.entcs.2005.04.040 fatcat:zswbcgplvbdspjwbx5bjpkiabu

Approximations of modal logics: K and beyond

Guilherme de Souza Rabello, Marcelo Finger
2008 Annals of Pure and Applied Logic  
A tableau-based proof system is presented, n-SST, and soundness and completeness is shown for the approximation of modal logics K, T, D, S4 and S5.  ...  Inspired by the recent work on approximations of classical logic, we present a method that approximates several modal logics in a modular way.  ...  As is usual in modal logics, by imposing several properties to the class of frames we obtain several approximated modal n-logics, such as K, T, D, S4 and S5.  ... 
doi:10.1016/j.apal.2007.11.009 fatcat:tshja6an2rbsrkhcz5lxultfda

A Logical Mix of Approximation and Separation [chapter]

Aquinas Hobor, Robert Dockins, Andrew W. Appel
2010 Lecture Notes in Computer Science  
If a model uses indirection, then its logic must reason about the resulting approximation; if a model contains substructure, then its logic often contains notations of separation.  ...  We show how to build program logics for settings involving approximation and/or separation. Our work is machine checked in Coq and available as part of the Mechanized Semantic Library.  ...  Readers familiar with modal logics will recognize (6) as axiom K, which is characteristic the "normal" modal logics.  ... 
doi:10.1007/978-3-642-17164-2_30 fatcat:hyoc62yburarjar3rsspufkstm

A Recursive Shortcut for CEGAR: Application To The Modal Logic K Satisfiability Problem

Jean-Marie Lagniez, Daniel Le Berre, Tiago de Lima, Valentin Montmirail
2017 Proceedings of the Twenty-Sixth International Joint Conference on Artificial Intelligence  
Then we propose a specific implementation of the RECAR approach to solve the modal logic K satisfiability problem.  ...  We implemented both a CEGAR and a RECAR approach for the modal logic K satisfiability problem within the solver MoSaiC.  ...  Part of this work was supported by the ANR project SATAS (ANR-15-CE40-0017), the French Ministry for Higher Education and Research and the Nord-Pas de Calais Regional Council through the "Contrat de PlanÉtat  ... 
doi:10.24963/ijcai.2017/94 dblp:conf/ijcai/LagniezBLM17 fatcat:k6wiboqer5gmzhhgxpnhvkfvba

Second-Order Quantifier Elimination in Modal Contexts [chapter]

Andrzej Szalas
2002 Lecture Notes in Computer Science  
In the current paper we generalize the result of [19] by allowing modal operators. This allows us to provide a unifying framework for many applications, that require the use of intensional concepts.  ...  databases, knowledge representation, commonsense reasoning and approximate reasoning.  ...  In the rest of the paper we shall always deal with formulas for which such fixpoints exist. Modal Logics In this paper we consider normal modal logics, i.e., extensions of logic K.  ... 
doi:10.1007/3-540-45757-7_19 fatcat:kqzab3gscrhmhoerd75lnz4bfq

Logical approaches to fuzzy similarity-based reasoning: an overview [chapter]

Lluís Godo, Ricardo O. Rodríguez
2008 Preferences and Similarities  
In particular, for these approximate entailments we provide four different formalisations in terms of suitable systems of modal and conditional logics, including for each class a system of graded operators  ...  We basically identify two different kinds of logical approaches that have been used to formalize fuzzy similarity reasoning: syntactically-oriented approaches based on a notion of approximate proof, and  ...  The authors also acknowledge partial support of  ... 
doi:10.1007/978-3-211-85432-7_4 fatcat:477lzy6blja3jaugsfnws7ozuq

Fixpoint 3-valued semantics for autoepistemic logic [article]

M. Denecker and V. Marek and M. Truszczynski
1999 arXiv   pre-print
In the case of modal representations of logic programs our least fixpoint semantics expresses well-founded semantics or 3-valued Fitting-Kunen semantics (depending on the embedding used).  ...  The paper presents a constructive fixpoint semantics for autoepistemic logic (AEL). This fixpoint characterizes a unique but possibly three-valued belief set of an autoepistemic theory.  ...  Autoepistemic logic -preliminaries The language of autoepistemic logic is the standard language of propositional modal logic over a set of atoms Σ and with a single modal operator K.  ... 
arXiv:cs/9901003v1 fatcat:fccqhyscj5fkjenbik3daxka6q

Fixpoint 3-valued semantics for autoepistemic logic [chapter]

Marc Denecker, V. Wiktor Marek, Mirosław Truszczyński
1999 Logical Foundations for Cognitive Agents  
In the case of modal representations of logic programs our least xpoint semantics expresses well-founded semantics or 3-valued Fitting-Kunen semantics (depending on the embedding used).  ...  We show that complete xpoints of the derivation operator correspond to Moore's stable expansions.  ...  Autoepistemic logic | preliminaries The language of autoepistemic logic is the standard language of propositional modal logic over a set of atoms and with a single modal operator K.  ... 
doi:10.1007/978-3-642-60211-5_10 fatcat:oncr6mcxyvcolc4r6yv43asss4

A Quantified Coalgebraic van Benthem Theorem [chapter]

Paul Wild, Lutz Schröder
2021 Lecture Notes in Computer Science  
w.r.t. behavioural distance, can be approximated by quantitative modal formulae of bounded rank.  ...  This result has recently been extended to two flavours of quantitative modal logic, viz. fuzzy modal logic and probabilistic modal logic.  ...  V-valued behavioural distance and expressible in V-valued coalgebraic (first-order) predicate logic can be approximated by V-valued modal formulae of bounded rank.  ... 
doi:10.1007/978-3-030-71995-1_28 fatcat:tjktmyewcrgpdmhyd64xgbvtrq

A van Benthem Theorem for Fuzzy Modal Logic [article]

Paul Wild, Lutz Schröder, Dirk Pattinson, Barbara König
2018 arXiv   pre-print
We present a fuzzy (or quantitative) version of the van Benthem theorem, which characterizes propositional modal logic as the bisimulation-invariant fragment of first-order logic.  ...  distance are exactly those that can be approximated by fuzzy modal formulas.  ...  We write L k for the set of modal formulas of rank at most k.  ... 
arXiv:1802.00478v2 fatcat:nypcw2p4kvefxefmrpv7vorsp4

Expressivity of Quantitative Modal Logics : Categorical Foundations via Codensity and Approximation

Yuichi Komorida, Shin-ya Katsumata, Clemens Kupke, Jurriaan Rot, Ichiro Hasuo
2021 2021 36th Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)  
A modal logic that is strong enough to fully characterize the behavior of a system is called expressive.  ...  Each of these quantitative expressivity results uses a tailor-made argument; distilling the essence of these arguments is non-trivial, yet important to support the design of expressive modal logics for  ...  and expressivity of modal logic.  ... 
doi:10.1109/lics52264.2021.9470656 fatcat:yfyv6dqxrnaexpkdlyz6ftlcsi

A Modal Characterization Theorem for a Probabilistic Fuzzy Description Logic

Paul Wild, Lutz Schröder, Dirk Pattinson, Barbara König
2019 Proceedings of the Twenty-Eighth International Joint Conference on Artificial Intelligence  
that modal logic is precisely the bisimulation-invariant fragment of first-order logic.  ...  Specifically, we show that every formula in probabilistic fuzzy first-order logic that is non-expansive wrt. behavioural distance can be approximated by concepts of bounded rank in probabilistic fuzzy  ...  can be approximated by fuzzy modal formulae of bounded rank.  ... 
doi:10.24963/ijcai.2019/263 dblp:conf/ijcai/WildSP019 fatcat:b74qeyfflzchbjgynfhkyca62y

Expressivity of Quantitative Modal Logics: Categorical Foundations via Codensity and Approximation [article]

Yuichi Komorida, Shin-ya Katsumata, Clemens Kupke, Jurriaan Rot, Ichiro Hasuo
2021 arXiv   pre-print
A modal logic that is strong enough to fully characterize the behavior of a system is called expressive.  ...  Each of these quantitative expressivity results uses a tailor-made argument; distilling the essence of these arguments is non-trivial, yet important to support the design of expressive modal logics for  ...  If the set { ϕ x | ϕ ∈ L S , depth(ϕ) ≤ i} ⊆ C(X, Ω) is approximating for each i, then S is expressive for x.  ... 
arXiv:2105.10164v1 fatcat:vnu7fq3tprbilmty6njig35pky

Uniform semantic treatment of default and autoepistemic logics

Marc Denecker, Victor W. Marek, Mirosław Truszczyński
2003 Artificial Intelligence  
The correspondence exploits the modal interpretation of a default proposed by Konolige.  ...  Our approach elucidates fundamental constructive principles in which agents form their belief sets, and leads to approximation semantics for autoepistemic and default logics.  ...  (the logical value of the modal atom Kϕ) is either t 4 or f 4 .  ... 
doi:10.1016/s0004-3702(02)00293-x fatcat:zpyvjdfugngkxloqxh6ma4pl7m

A van Benthem Theorem for Quantitative Probabilistic Modal Logic [article]

Paul Wild, Lutz Schröder, Dirk Pattinson, Barbara König
2019 arXiv   pre-print
first-order logic; more precisely, bisimulation-invariant first-order formulas are approximable by modal formulas of bounded rank.  ...  , which states that modal logic is precisely the bisimulation-invariant fragment of first-order logic.  ...  expressible in fuzzy first-order logic can be approximated by formulas in fuzzy modal logic of bounded modal rank [45] .  ... 
arXiv:1810.04722v2 fatcat:wu4kpdw4d5btzmi2hiwz72fdqu
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