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### Labelled Tableaux for Non-Normal Modal Logics [chapter]

Guido Governatori, Alessandro Luppi
2000 Lecture Notes in Computer Science
In this paper we show how to extend KEM, a tableau-like proof system for normal modal logic, in order to deal with classes of non-normal modal logics, such as monotonic and regular, in a uniform and modular  ...  Acknowledgments We would like to thank Giovanna Corsi for her helpful discussions. This research was partially supported by the Australian Research Council under Large Grant No. A49803544.  ...  represented by a non-normal modal logic [2] .  ...

### Labelled modal tableaux

Guido Governatori
Specifically in the second part we show how labelled tableaux (KEM) can account for different types of logics (e.g., non-normal modal logics and conditional logics).  ...  Labelled tableaux are extensions of semantic tableaux with annotations (labels, indices) whose main function is to enrich the modal object language with semantic elements.  ...  In Section 3 we examine how to extend labelled tableaux to cover other logics having possible world semantics, namely non-normal modal logic (modal logic where necessitation does not hold) and conditional  ...

### A Fibred Tableau Calculus for Modal Logics of Agents [chapter]

2006 Lecture Notes in Computer Science
Having done that we show how to uniformly construct a tableau calculus for the combined logic using Governatori's labelled tableau system KEM. We conclude with a discussion on KEM's features. M.  ...  In this paper we extend the above mentioned works by providing a tableau-based proof technique for the combined/fibred logics.  ...  multi-modal logic for multi-agent systems.  ...

### Strongly analytic tableaux for normal modal logics [chapter]

Fabio Massacci
1994 Lecture Notes in Computer Science
A strong analytic tableau calculus is presentend for the most common normal modal logics. The method combines the advantages of both sequent-like tableaux and pre xed tableaux.  ...  Proper rules are used, instead of complex closure operations for the accessibility relation, while non determinism and cut rules, used by sequent-like tableaux, are totally eliminated.  ...  Pirri for reading drafts of this paper and for their many useful hints and suggestions. Comments from W. Bibel and anonymous referees helped to improve the presentation of this paper.  ...

### On the Relative Complexity of Labelled Modal Tableaux

Guido Governatori
2003 Electronical Notes in Theoretical Computer Science
We investigate the relative complexity of two free-variable labelled modal tableaux (KEM and Single Step Tableaux, SST).  ...  We discuss the reasons why p-simulation is not a proper measure of the relative complexity of tableaux-like proof systems, and we propose an improved comparison scale (p-search-simulation).  ...  In this paper we perform a theoretical comparison of two labelled tableaux for modal logic.  ...

### Page 1994 of Mathematical Reviews Vol. , Issue 96d [page]

1996 Mathematical Reviews
Non-Classical Logics 5 (1995), no. 1, 77-96. Summary: “The major emphasis of this paper is on the defini- tion of complete strategies in tableaux calculi for propositional modal logics.  ...  Perry Smith (1-MR; Ann Arbor, MI) 96d:03021 03B35 03845 Demri, Stéphane (F-GREN-AI; Grenoble) Uniform and nonuniform strategies for tableaux calculi for modal logics. (English summary) J. Appl.  ...

### On Constructing Fibred Tableaux for BDI Logics [chapter]

2006 Lecture Notes in Computer Science
(non-normal modal logic [10], multi-modal logics [9] and conditional logics [2]).  ...  We show how to uniformly construct a tableau calculus for the combined logic using Governatori's labelled tableau system KEM. with a large class of intensional logics admitting possible world semantics  ...  Notice, however, that the fibring construction given in [11, 13] works for normal (multi-)modal logics as well as non-normal modal logics.  ...

### Certification of Prefixed Tableau Proofs for Modal Logic

Tomer Libal, Marco Volpe
2016 Electronic Proceedings in Theoretical Computer Science
modal proofs given in labeled sequent calculi, prefixed tableaux and free-variable prefixed tableaux.  ...  We describe the general method for the logic K, present its implementation in a prolog-like language, provide some examples and discuss how to extend the approach to other normal modal logics  ...  Prefixed tableaux for modal logic 2.3.1 Modal logic The language of (propositional) modal formulas consists of a functionally complete set of classical propositional connectives, a modal operator (here  ...

### Automated Reasoning over Deontic Action Logics with Finite Vocabularies

Pablo F. Castro, Thomas S. E. Maibaum
2014 Electronic Proceedings in Theoretical Computer Science
In this paper we investigate further the tableaux system for a deontic action logic we presented in previous work.  ...  This tableaux system uses atoms (of a given boolean algebra of action terms) as labels of formulae, this allows us to embrace parallel execution of actions and action complement, two action operators that  ...  Labeled systems are usual for many logics and tableaux systems, an introduction to these systems can be found in [10, 11] .  ...

### An efficient relational deductive system for propositional non-classical logics

Andrea Formisano, Marianna Nicolosi-Asmundo
2006 Journal of Applied Non-Classical Logics
Non-Classical Logics.) Università di L'Aquila,  ...  We describe a relational framework that uniformly supports formalization and automated reasoning in various propositional modal logics.  ...  Acknowledgements We thank Martin Giese, Joanna Golińska, Rajeev Goré, and Ewa Or lowska for useful discussions on the topics of this paper.  ...

### Non-Normal Dialogics for a Wonderful World and More [chapter]

Shahid Rahman
2006 The Age of Alternative Logics
involved in the application of the so-called Hintikka strategy and hybrid languages while constructing tableau-systems for non-normal modal logics.  ...  The aim of the paper is to offer a dialogical interpretation of non-normal modal logic which will suggest some explorations beyond the concept of nonnormality.  ...  Also thanks to Laurent Keiff (Lille 3) for interesting and lively discussions.  ...

### Introducing Reactive Modal Tableaux [chapter]

Dov M. Gabbay
2013 Reactive Kripke Semantics
This paper introduces the idea of reactive semantics and reactive Beth tableaux for modal logic and quotes some of its applications. The reactive idea is very simple.  ...  If our starting point is s 0 , and the path is s 0 , s 1 , . . . , s n , then the system is ordinary non-reactive system if the options available at s n (i.e., which states t we can go to from s n ) do  ...  Acknowledgements I am grateful to Johan van Benthem and the referees for helpful criticism and useful suggestions.  ...

### Introducing reactive modal tableaux

Dov Gabbay
2012 Annals of Mathematics and Artificial Intelligence
This paper introduces the idea of reactive semantics and reactive Beth tableaux for modal logic and quotes some of its applications. The reactive idea is very simple.  ...  If our starting point is s 0 , and the path is s 0 , s 1 , . . . , s n , then the system is ordinary non-reactive system if the options available at s n (i.e., which states t we can go to from s n ) do  ...  Acknowledgements I am grateful to Johan van Benthem and the referees for helpful criticism and useful suggestions.  ...

### Page 5453 of Mathematical Reviews Vol. , Issue 2002H [page]

2002 Mathematical Reviews
This work exploits the connection between our normalizing labelled natural deduction systems and cut-free labelled sequent systems.  ...  Vigano, Studia Logica 60 (1998), no. 1, 119-160; MR 99f:03007}, we introduced a framework for the uniform formalization of large families of non-classical logics with Kripke semantics, such as modal, relevance  ...

### Page 8092 of Mathematical Reviews Vol. , Issue 98M [page]

1998 Mathematical Reviews
Extending first-order CTL for handling action labels, we define a multi-modal logic MCTL which is well suited for specify- ing transition systems and their properties.  ...  We present sound and complete tableau systems for these problems and compare them to non-tableau algorithms.”  ...
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