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Introducing Polymodal Neighbourhood Logics

Renata de Freitas, Petrucio Viana
2009 Electronical Notes in Theoretical Computer Science  
We provide a completeness result for the basic polymodal neighbourhood system and show how some important systems based on neighbourhood like semantics can be simulated as subsystems of ours.  ...  In this paper, we start the study of polymodal neighbourhood languages.  ...  Acknowledgement Thanks are due to Systems and Computer Engineering Program of COPPE/UFRJ, which facilities made this research possible.  ... 
doi:10.1016/j.entcs.2009.07.048 fatcat:csj7ch6jnzdh3dcfetd4nvdts4

INSTANTIAL NEIGHBOURHOOD LOGIC

JOHAN VAN BENTHEM, NICK BEZHANISHVILI, SEBASTIAN ENQVIST, JUNHUA YU
2016 The Review of Symbolic Logic  
The resulting system of 'instantial neighbourhood logic' INL has a nontrivial mix of features from relational semantics and from neighbourhood semantics.  ...  We explore some basic model-theoretic behavior, including a matching notion of bisimulation, and give a complete axiom system for which we prove completeness by a new normal form technique.  ...  The answer lies in a number of faithful translations. In this section we show how to embed the basic modal logic K and the basic neighbourhood logic E into INL.  ... 
doi:10.1017/s1755020316000447 fatcat:lf3hiayifzc4hdg4ttonwe7gn4

Generalized topological semantics for weak modal logics [article]

Tomasz Witczak
2020 arXiv   pre-print
Moreover, the whole universe does not need to be open. We use modified version of this framework to establish certain models for non-normal modal logics.  ...  The second one leads to the quite known logics MT4 and MNT4. We obtain some completeness results and we prove correspondence between different classes of frames.  ...  This is a connection between non-normal modal logics and the theory of rough sets or approximate reasoning.  ... 
arXiv:1904.06099v5 fatcat:dbxzlfg23zchhipssh32z4tlku

A Van Benthem/Rosen theorem for coalgebraic predicate logic

Lutz Schröder, Dirk Pattinson, Tadeusz Litak
2015 Journal of Logic and Computation  
As instances of this generic result, we obtain corresponding characterizations for, e.g., conditional logic, neighbourhood logic (i.e., classical modal logic), and monotone modal logic.  ...  Coalgebraic modal logic serves as a unifying framework to study a wide range of modal logics beyond the relational realm, including probabilistic and graded logics as well as conditional logics and logics  ...  The authors wish to thank Helle Hvid Hansen for useful discussions and pointers to the literature and to Erwin R. Catesbeiana for elaborating on the role of ⊥ T .  ... 
doi:10.1093/logcom/exv043 fatcat:45y2yfbwzbcgnj6ys544ti4cm4

Sequent Calculi and Interpolation for Non-Normal Modal and Deontic Logics

Eugenio Orlandelli
2020 Logic and Logical Philosophy  
G3-style sequent calculi for the logics in the cube of non-normal modal logics and for their deontic extensions are studied.  ...  Finally, a Maehara-style proof of Craig's interpolation theorem for most of the logics considered is given.  ...  Partially supported by the Academy of Finland, research project no. 1308664. Thanks are due to Tiziano Dalmonte, Simone Martini, and two anonymous referees for many helpful suggestions.  ... 
doi:10.12775/llp.2020.018 fatcat:qi3ijgiwwjag3murwosx3eotiq

A Modal Logic for Coalitional Power in Games

M. Pauly
2002 Journal of Logic and Computation  
and non-normal modal logics correspond to 1-and 2-player versions of Coalition Logic.  ...  We propose a modal logic (Coalition Logic) to formalize reasoning about effectivity in game frames, where ³ expresses that coalition is effective for ³.  ...  Acknowledgements I thank Johan van Benthem, Peter van Emde Boas, Rohit Parikh, Yde Venema and the anonymous referees for comments on earlier drafts of this paper.  ... 
doi:10.1093/logcom/12.1.149 fatcat:qqqcgbnuxfghvcac3rlzesngru

Special Issue on Hybrid Logics

Carlos Areces, Patrick Blackburn
2010 Journal of Applied Logic  
Coinductive models and normal forms for modal logics by C. Areces and D. Gorín.  ...  In this article, the author pursues the goal to combine these two ideas into a single system, and present a hybrid justification version of the modal logic T, providing a semantics, a proof theory, a completeness  ... 
doi:10.1016/j.jal.2010.10.001 fatcat:zqbmgbrokvel5jrjrkym3bg3vy

Neighbourhood semantics and axioms for strategic fragment of classical stit logic [article]

Daniil Khaitovich
2022 arXiv   pre-print
The neighbourhood semantics for the fragment is presented, accompanied with the soundness, canoniciy hence strong completeness results.  ...  In comparison with other multi-agent modal logics, the main advantage of STIT theories is expressive power.  ...  Basic theory of sees to it that The language of "classical" stit logic L cstit is defined as follows.  ... 
arXiv:2203.09225v1 fatcat:idnheh7hejfodp3v7f3kpqrn3i

Structures for Epistemic Logic [chapter]

Nick Bezhanishvili, Wiebe van der Hoek
2014 Outstanding Contributions to Logic  
In this paper we overview the main structures of epistemic and doxastic logic. We start by discussing the most celebrated models for epistemic logic, i.e., epistemic Kripke structures.  ...  In particular, we discuss here neighbourhood semantics and topological semantics.  ...  Acknowledgement The first author would like to thank Guram Bezhanishvili, David Gabelaia, Ian Hodkinson, Clemens Kupke and Levan Uridia for many in-  ... 
doi:10.1007/978-3-319-06025-5_12 fatcat:d34ea3o3bncgnok4j7ecek4v6q

Substructural epistemic logics

Igor Sedlár
2015 Journal of Applied Non-Classical Logics  
The logics combine normal modal epistemic logics (implicit belief) with distributive substructural logics (available evidence).  ...  The main technical result is a general completeness theorem. Axiomatizations are provided by means of twosorted Hilbert-style calculi.  ...  Portions of the article have been presented at informal workshops and seminars at the Department of Applied Informatics, Comenius University in Bratislava; Department of Logic, Charles University in Prague  ... 
doi:10.1080/11663081.2015.1094313 fatcat:5wdmi7ffm5axhkhxdtkcgktyjq

Possible World Semantics for Defeasible Deontic Logic [chapter]

Guido Governatori, Antonino Rotolo, Erica Calardo
2012 Lecture Notes in Computer Science  
Traditionally defeasible logics are defined proof theoretically based on the proof conditions for the logic.  ...  Section 4 discusses how to interpret Defeasible Multi-modal Logic in neighbourhood semantics and identifies one open problem. 2 Defeasible Deontic Logic: An Informal Presentation DL has three basic kinds  ...  Acknowledement NICTA is funded by the Australian Government as represented by the Department of Broadband, Communications and the Digital Economy and the Australian Research Council through the ICT Centre  ... 
doi:10.1007/978-3-642-31570-1_4 fatcat:eixxckbqtngkxhqshc3gwkjewu

On the Axiomatisation of Elgesem's Logic of Agency and Ability

Guido Governatori, Antonino Rotolo
2005 Journal of Philosophical Logic  
This is done by examining Elgesem's modal logic of agency and ability using semantics with different flavours.  ...  In this paper we show that the Hilbert system of agency and ability presented by Dag Elgesem is incomplete with respect to the intended semantics.  ...  Acknowledgements Preliminary versions of this paper were presented at the Annual Meeting of the Australasian Association for Logic (Dunedin, New Zealand, 17-18 January 2004) and at Advances in Modal Logic  ... 
doi:10.1007/s10992-004-6368-1 fatcat:sbd7enkjhrdz5g4ugq7hwzpliq

Mathematical modal logic: A view of its evolution [chapter]

Robert Goldblatt
2006 Handbook of the History of Logic  
This is a survey of the origins of mathematical interpretations of modal logics, and their development over the last century or so.  ...  It concludes with an account of several applications of modal model theory to mathematics and theoretical computer science.  ...  For such assistance I thank Wim Blok, Max Cresswell, John Dawson, Allen Emerson, Saul Kripke, Neil Leslie, Ed Mares, Robin Milner, Hiroakira Ono, Lawrence Pedersen, Vaughan Pratt, Colin Stirling and Paul  ... 
doi:10.1016/s1874-5857(06)80027-0 fatcat:dihvhmx5vjhdjndl7x5auvqbki

Mathematical modal logic: A view of its evolution

Robert Goldblatt
2003 Journal of Applied Logic  
This is a survey of the origins of mathematical interpretations of modal logics, and their development over the last century or so.  ...  It concludes with an account of several applications of modal model theory to mathematics and theoretical computer science.  ...  For such assistance I thank Wim Blok, Max Cresswell, John Dawson, Allen Emerson, Saul Kripke, Neil Leslie, Ed Mares, Robin Milner, Hiroakira Ono, Lawrence Pedersen, Vaughan Pratt, Colin Stirling and Paul  ... 
doi:10.1016/s1570-8683(03)00008-9 fatcat:zhwzfvdeqjg3rgbkqstbxk5yqq

A Coalgebraic Perspective on Monotone Modal Logic

Helle Hvid Hansen, Clemens Kupke
2004 Electronical Notes in Theoretical Computer Science  
In particular, we show that the UpP-functor does not preserve weak pullbacks, and we prove interpolation for a number of monotone modal logics using results on UpP-bisimulations.  ...  The paper has two main parts: First we make the connection between monotone modal logic and the general theory of coalgebras precise by defining functors UpP : Set → Set and UpV : Stone → Stone such that  ...  Monotone modal logic We assume the reader is familiar with normal modal logic [4] and refer to [5, 12] for non-normal modal logic.  ... 
doi:10.1016/j.entcs.2004.02.028 fatcat:sobmaoiz4renfnbkip6mii4vja
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