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Alternating Set Quantifiers in Modal Logic [article]

Fabian Reiter
2016 arXiv   pre-print
We establish the strictness of several set quantifier alternation hierarchies that are based on modal logic, evaluated on various classes of finite graphs.  ...  This extends to the modal setting a celebrated result of Matz, Schweikardt and Thomas (2002), which states that the analogous hierarchy of monadic second-order logic is strict.  ...  Furthermore, I am grateful to Charles Paperman and an anonymous reviewer of my previous paper, who both suggested that there might be a connection between distributed graph automata and modal logic.  ... 
arXiv:1602.08971v1 fatcat:sum4d4tp5zhwvjsafg4oh2zfwm

The Complexity of One-Agent Refinement Modal Logic [chapter]

Laura Bozzelli, Hans van Ditmarsch, Sophie Pinchinat
2012 Lecture Notes in Computer Science  
We investigate the complexity of satisfiability for one-agent refinement modal logic (RML), an extension of basic modal logic (ML) obtained by adding refinement quantifiers on structures.  ...  is based was the recipient of the best paper award of the 2012 JELIA conference in Toulouse [Bozzelli et al., 2012b].  ...  subsets definable in the logical language (of basic modalities and quantifiers), and quantifying over all subsets.  ... 
doi:10.1007/978-3-642-33353-8_10 fatcat:yz3utqkphfcyzos32sl2jkbpga

The complexity of one-agent refinement modal logic

Laura Bozzelli, Hans van Ditmarsch, Sophie Pinchinat
2015 Theoretical Computer Science  
We investigate the complexity of satisfiability for one-agent refinement modal logic (RML), an extension of basic modal logic (ML) obtained by adding refinement quantifiers on structures.  ...  is based was the recipient of the best paper award of the 2012 JELIA conference in Toulouse [Bozzelli et al., 2012b].  ...  subsets definable in the logical language (of basic modalities and quantifiers), and quantifying over all subsets.  ... 
doi:10.1016/j.tcs.2015.07.015 fatcat:snz2vuj64nbw3iyfx5ppbilrji

A Model Checker for Value-Passing Mu-Calculus Using Logic Programming [chapter]

C. R. Ramakrishnan
2001 Lecture Notes in Computer Science  
In particular, we present valuepassing modal mu-calculus, its formal semantics and describe a natural implementation of this semantics as a logic program.  ...  In this paper, we explore the use of data variables in the property logic.  ...  In this paper, we describe how the model checker in XMC can be extended to handle the value-passing modal mu-calculus, a logic that permits quantified data variables.  ... 
doi:10.1007/3-540-45241-9_1 fatcat:2oelfds5o5agvcch5oeozwmzru

Pluralities and Sets

Øystein Linnebo
2010 Journal of Philosophy  
In plural first-order logic we have in addition plural variables such as xx and yy, which can also be bound by existential and universal quantifiers to yield so-called plural quantifiers. 1 '∃xx' is read  ...  In ordinary singular first-order logic we have singular variables such as x and y, which can be bound by the existential and universal quantifiers.  ...  non-modal logic encapsulated in L.  ... 
doi:10.5840/jphil2010107311 fatcat:qv23nydk4bdq5jpoi33ltolihe

Modal Nonmonotonic Logics Revisited: Efficient Encodings for the Basic Reasoning Tasks [chapter]

Thomas Eiter, Volker Klotz, Hans Tompits, Stefan Woltran
2002 Lecture Notes in Computer Science  
In this paper, we show how variants of Moore's autoepistemic logic can be axiomatised by means of quantified Boolean formulas (QBFs).  ...  Modal nonmonotonic logics constitute a well-known family of knowledge-representation formalisms capturing ideally rational agents reasoning about their own beliefs.  ...  In fact, the evaluation problem for QBFs having prenex normal form with i − 1 quantifier alternations is complete for the i-th level of the polynomial hierarchy.  ... 
doi:10.1007/3-540-45616-3_8 fatcat:5yzrmskpq5a45j7tzrch6qj6ja

Logics for Dependence and Independence (Dagstuhl Seminar 15261)

Erich Grädel, Juha Kontinen, Jouka Väänänen, Heribert Vollmer, Marc Herbstritt
2016 Dagstuhl Reports  
A key objective of the seminar was to bring together researchers working in dependence logic and in the application areas so that they can communicate state-of-the-art advances and embark on a systematic  ...  This report documents the programme and outcomes of Dagstuhl Seminar 15261 'Logics for Dependence and Independence'.  ...  time with polynomially many alternations.  ... 
doi:10.4230/dagrep.5.6.70 dblp:journals/dagstuhl-reports/GradelKVV15 fatcat:wqkpzm2ywbcjdke2zyvvw4dlny

Are the Validities of Modal Logic Analytic? Or Analyticity Again, through Information, Proof, Modal Logic and Hintikka

Francesca Poggiolesi
2015 Philosophia Scientiæ  
Basic maximal consistent sets represent the infinite proper formal counterpart of the idea of alternative concerning the world in the framework of modal logic.  ...  Each propositional constituent constructed from p i is a modal constituent. we affirm that in modal logic we cannot draw a finite list of basic maximal consistent sets, i.e. of alternatives concerning  ... 
doi:10.4000/philosophiascientiae.1110 fatcat:5cigo4ctmnejhgmebtojwfd3pa

Page 1788 of Mathematical Reviews Vol. , Issue 85e [page]

1985 Mathematical Reviews  
But also, in the intended models, each predicate is assigned a set of extensions, reflecting its possible behaviours. Then, two alternatives are presented.  ...  For any regular propositional modal logic L let K'")(L) be the class of all n-modal (n — 1)-fold products of first-order frames in which all L-formulas are valid.  ... 

21 Modal logic and philosophy [chapter]

Sten Lindström, Krister Segerberg
2007 Studies in Logic and Practical Reasoning  
Lindström's work was supported by The Bank of Sweden Tercentenary Foundation via the research project "Medvetande, Materialism och Möjlighet" ("Mind, Materialism, and Modality").  ...  BIBLIOGRAPHY The following bibliography contains not only references in the narrow sense of being explicitly referred to in the main text but also a number of works that it has seemed important to include  ...  In the same year, Jaakko Hintikka published two papers on the semantics of quantified modal logic: 'Modality as referential multiplicity' and 'Quantifiers in deontic logic' (Hintikka [39, 40] ).  ... 
doi:10.1016/s1570-2464(07)80024-3 fatcat:iscc6l6otncqxduh63eln3lts4

Universal quantifier PPIs

Hedde Zeijlstra
2017 Glossa  
Why have Positive Polarity Items (PPIs) that are universal quantifiers only been attested in the domain of modal auxiliaries (cf.  ...  In this paper, I argue that universal quantifier PPIs actually do exist, both in the domain of quantifiers over individuals and in the domain of quantifiers over possible worlds, as, I argue, is predicted  ...  Since in Downward Entailing (DE) contexts logical entailments relations are reversed, all stronger alternatives become weaker, and therefore no contradiction arises. (3) ∃x.  ... 
doi:10.5334/gjgl.220 fatcat:gblewego7ndolejrukybd6m5te

Validity and Entailment in Modal and Propositional Dependence Logics [article]

Miika Hannula
2019 arXiv   pre-print
In particular, we address the question of the complexity of validity in modal dependence logic.  ...  The logics examined are obtained by extending the standard modal and propositional logics with notions of dependence, independence, and inclusion in the team semantics context.  ...  in the quantified propositional setting iff they are satisfied by X and the structure {0, 1} in the first-order setting.  ... 
arXiv:1608.04301v5 fatcat:vedbmg5cjjhenf4wlmujidgxe4

Symbolic Decision Procedures for QBF [chapter]

Guoqiang Pan, Moshe Y. Vardi
2004 Lecture Notes in Computer Science  
In this work we explore an alternative approach to QBF solving, based on symbolic quantifier elimination.  ...  In both approaches, QBF formulas are solved by eliminating all their quantifiers.  ...  Using translation from modal logic allowed construction of high alternation-depth problems that are both non-trivial and tractable.  ... 
doi:10.1007/978-3-540-30201-8_34 fatcat:qh6tulx5mrelfj2cm6abw5qkty

Validity and Entailment in Modal and Propositional Dependence Logics

Miika Hannula, Marc Herbstritt
2017 Annual Conference for Computer Science Logic  
In particular, we address the question of the complexity of validity in modal dependence logic.  ...  Furthermore, we show that this result applies to the extension of propositional dependence logic with quantifiers as well as to the so-called extended modal logic which can express dependencies between  ...  in the quantified propositional setting iff they are satisfied by X and the structure {0, 1} in the first-order setting.  ... 
doi:10.4230/lipics.csl.2017.28 dblp:conf/csl/Hannula17 fatcat:5q6fmjg4bzdnbal3e3gonibn2m

Design and Results of TANCS-2000 Non-classical (Modal) Systems Comparison [chapter]

Fabio Massacci, Francesco M. Donini
2000 Lecture Notes in Computer Science  
The aim of the TABLEAUX-2000 Non-Classical (Modal) System Comparisons (TANCS-2000) is to provide a set of benchmarks and a standardized methodology for the assessment and comparison of ATP systems in non-classical  ...  logics, as it is done for first-order logic with the CADE System Competition.  ...  use of nominals in modal logics.  ... 
doi:10.1007/10722086_4 fatcat:m435csjttrculkccaoempvo5re
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