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First-Order Resolution Methods for Modal Logics [chapter]

Renate A. Schmidt, Ullrich Hustadt
2013 Lecture Notes in Computer Science  
Without going into too much detail, we survey different ways of translating modal logics into first-order logic, we explore different ways of using first-order resolution theorem provers, and we discuss  ...  In this paper we give an overview of results for modal logic which can be shown using techniques and methods from first-order logic and resolution.  ...  The axiomatic translation has the advantage that it can reduce also second-order modal logics to first-order logic.  ... 
doi:10.1007/978-3-642-37651-1_15 fatcat:pta3fxqsnfal3cigcnryyxjcba

Translation Methods for Non-Classical Logics: An Overview

HANS JŪRGEN OHLBACH
1993 Logic Journal of the IGPL  
In the second part of the paper it is shown how to translate Hilbert axioms into properties of the semantic structure and vice versa, i.e. we can automate important parts of correspondence theory.  ...  Optimized 'functional' and semi-functional translation into predicate logic is described.  ...  The comments of various referees were also very helpful.  ... 
doi:10.1093/jigpal/1.1.69 fatcat:ykf5l4ndaffwxdjtgoztnm6jte

Page 5554 of Mathematical Reviews Vol. , Issue 94j [page]

1994 Mathematical Reviews  
Summary: “The functional translation from modal logic into first- order predicate logic is revised.  ...  Second, we do not need to add anything to the logic of knowledge: the ‘right’ properties of belief fall out of our definitions and the properties of knowledge.  ... 

Computer Support for the Development and Investigation of Logics

Hans Jürgen Ohlbach
1996 Logic Journal of the IGPL  
The development and investigation of application{oriented logics comprises many aspects and problems.  ...  In particular, we consider the correspondences between axiomatic and semantic speci cations of a logic and the problem of nding one from the other by means of automated theorem provers and quanti er elimination  ...  Thorsten Engel implemented the SCAN algorithm by modifying the Otter theorem prover and integrating an unskolemization algorithm.  ... 
doi:10.1093/jigpal/4.1.109 fatcat:zbub4nyly5ardizjv54ehe2kiy

Polynomial hierarchy graph properties in hybrid logic

F.M. Ferreira, C.M. Freire, M.R.F. Benevides, L. Menasché Schechter, A.T. Martins
2014 Journal of computer and system sciences (Print)  
In this article, we show that for each property of graphs G in the Polynomial Hierarchy (PH) there is a sequence φ 1 , φ 2 , . . . of formulas of the full hybrid logic which are satisfied exactly by the  ...  frames in G.  ...  Acknowledgements We would like to thank the anonymous referee for its detailed comments and suggestions.  ... 
doi:10.1016/j.jcss.2014.04.003 fatcat:knqjit3fzvdgnkkrjcvotukywe

Page 16 of Mathematical Reviews Vol. , Issue 98A [page]

1998 Mathematical Reviews  
There are well-known first-order con- ditions on the frame for several normal modal logics, but it is not immediate how to give a first-order translation for nonnormal modal logics.  ...  with respect to the known semantical properties of Kripke frames.  ... 

A bimodal perspective on possibility semantics

Johan van Benthem, Nick Bezhanishvili, Wesley H. Holliday
2016 Journal of Logic and Computation  
In particular, we define a full and faithful translation of the basic modal logic K over possibility models into a bimodal logic of partial functions over partial orders, and we show how to modulate this  ...  Moreover, our analysis clarifies the interplay between the complexity of translations and axiomatizations of the corresponding logics: adding axioms to the target bimodal logic simplifies translations,  ...  Acknowledgements We wish to thank Guram Bezhanishvili and the three anonymous referees of this paper for helpful comments.  ... 
doi:10.1093/logcom/exw024 fatcat:paao4gu5efclhcvsybgrb7c5nq

Page 6530 of Mathematical Reviews Vol. , Issue 2003i [page]

2003 Mathematical Reviews  
QSSz—, QS5z and QS5z-+ are the logics determined by these classes of models. The third system is shown to be easily translatable into the second.  ...  Certain properties of Q cannot be characterized using modal formulas, most notably, irreflexivity is modally undefinable; hence, sometimes irreflexivity may be added to the frame without loss of soundness  ... 

Deciding regular grammar logics with converse through first-order logic [article]

Stephane Demri, Hans de Nivelle
2004 arXiv   pre-print
This translation is theoretically interesting because it translates modal logics with certain frame conditions into first-order logic, without explicitly expressing the frame conditions.  ...  We provide a simple translation of the satisfiability problem for regular grammar logics with converse into GF2, which is the intersection of the guarded fragment and the 2-variable fragment of first-order  ...  (to quote a few modal logics in PSPACE, see e.g. [CZ97]). 3. Can our translation method be extended to first-order modal logics? 4. Can it be extended to first-order intuitionistic logic? 5.  ... 
arXiv:cs/0306117v2 fatcat:zshbraohbbeybh2rgpohohrrha

Hybrid Logics and NP Graph Properties [chapter]

Francicleber Martins Ferreira, Cibele Matos Freire, Mario R. F. Benevides, L. Menasché Schechter, Ana Teresa Martins
2011 Lecture Notes in Computer Science  
We show that for each property of graphs G in NP there is a sequence φ 1 , φ 2 , . . . of formulas of the full hybrid logic which are satisfied exactly by the frames in G.  ...  These results lead to the definition of syntactically defined fragments of hybrid logic whose model checking problem is complete for each degree in the polynomial hierarchy.  ...  The translation given in Section 4 above can be used to produce hybrid formulas of polynomial size using formulas of second-order logic.  ... 
doi:10.1007/978-3-642-20920-8_15 fatcat:665g5saazfew3flvcaackknim4

Page 5631 of Mathematical Reviews Vol. , Issue 88k [page]

1988 Mathematical Reviews  
(2) When can a given first-order property be defined by a modal formula (or a set of modal formulas)? (3) Which classes of frames are definable by modal formulas?  ...  A modal formula determines the class of frames on which it holds, and in some cases this same class is defined by a first-order sentence.  ... 

Mechanised Reasoning and Model Generation for Extended Modal Logics [chapter]

Renate A. Schmidt, Ullrich Hustadt
2003 Lecture Notes in Computer Science  
The approach presented in this overview paper exploits that modal logics can be seen to be fragments of first-order logic and deductive methods can be developed and studied within the framework of firstorder  ...  We focus on a class of extended modal logics very similar in spirit to propositional dynamic logic and closely related to description logics.  ...  Acknowledgements We thank Hans de Nivelle, coauthor of the survey [16] on which a part of this text is based. We also thank the reviewer for helpful comments.  ... 
doi:10.1007/978-3-540-24615-2_3 fatcat:jypyr3tokzhh7erjlyu5faipsi

Logically Possible Worlds and Counterpart Semantics for Modal Logic [chapter]

Marcus Kracht, Oliver Kutz
2007 Philosophy of Logic  
The paper reviews the technical results from modal logic as well as their philosophical significance.  ...  It focuses on possible worlds semantics in general and on the notion of a possible world, of accessibility, and object. Contents  ...  This translation reduces intuitionistic logic to modal logic. In the background, however, we have a second reduction, that of modal logic to first-order logic, the standard translation.  ... 
doi:10.1016/b978-044451541-4/50025-7 fatcat:6ge4dvigzjgt7c77pbecm22faa

Modal deduction in second-order logic and set theory - I

J van Benthem
1997 Journal of Logic and Computation  
In this paper, this approach is shown equivalent to working with standard first-order translations of modal formulae in a theory of general frames.  ...  We investigate modal deduction through translation into standard logic and set theory.  ...  The semantics of weak second-order logic employs a straightforward modification of general frames.  ... 
doi:10.1093/logcom/7.2.251 fatcat:f7yqrxrsabfttdwhvitcdqlc4u

Representation, reasoning, and relational structures: a hybrid logic manifesto

P Blackburn
2000 Logic Journal of the IGPL  
This paper is about the good side of modal logic, the bad side of modal logic, and how hybrid logic takes the good and fixes the bad.  ...  On the contrary, we can talk about models using any classical language we find useful (for example, a first-order, infinitary, fixpoint, or second-order language).  ...  Acknowledgments In writing this paper I have tried to remain faithful to the spirit of my M4M talk, which means I have drawn on many discussions of modal logic, relational structures, hybrid logic, and  ... 
doi:10.1093/jigpal/8.3.339 fatcat:knzw6fq32bhd3dwhpkleufrm6y
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