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Resolution for hybrid logics

Stanislovas Norgėla
2011 Lietuvos matematikos rinkinys  
We describe a resolution method and a procedure to transform formulae of some pure hybrid logics into their clausal form.  ...  Resolution method become much simpler.  ...  This transformation is the basis for the resolution calculus for modal logic S4 presented in [7] .  ... 
doi:10.15388/lmr.2011.ml06 fatcat:mxlw5p6emfhhtll6hpgrtrehs4

A Principle for Incorporating Axioms into the First-Order Translation of Modal Formulae [chapter]

Renate A. Schmidt, Ullrich Hustadt
2003 Lecture Notes in Computer Science  
In this paper we present a translation principle, called the axiomatic translation, for reducing propositional modal logics with background theories, including triangular properties such as transitivity  ...  , Euclideanness and functionality, to decidable logics.  ...  The system combines temporal resolution for the temporal formulae and first-order resolution on the modal formulae.  ... 
doi:10.1007/978-3-540-45085-6_36 fatcat:l4qebca3gba4xpz3exmdfzg3i4

First-Order Resolution Methods for Modal Logics [chapter]

Renate A. Schmidt, Ullrich Hustadt
2013 Lecture Notes in Computer Science  
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.  ...  Because of the breadth of the area and the many applications we focus on the use of first-order resolution methods for modal logics.  ...  Let ϕ be a modal formula in negation normal form and let N be the clausal form of π sf (ϕ, ǫ) ∧ SF(∆).  ... 
doi:10.1007/978-3-642-37651-1_15 fatcat:pta3fxqsnfal3cigcnryyxjcba

Implementing Temporal Logics: Tools for Execution and Proof [chapter]

Michael Fisher
2006 Lecture Notes in Computer Science  
I thank them all for their endeavours. Summary We have overviewed a selection of tools for execution and proof within temporal logic.  ...  this work has been supported by funding from the Engineering and Physical Sciences Research Council (EPSRC) 1 , and has involved collaboration with a variety of outstanding colleagues from within the Logic  ...  Implementations Clausal Temporal Resolution The essential complexity in carrying out clausal temporal resolution is implementing the temporal resolution rule itself.  ... 
doi:10.1007/11750734_8 fatcat:dnerita2qfcevnmo3ah62kf24m

Modal resolution in clausal form

Patrice Enjalbert, Luis Farinas del Cerro
1989 Theoretical Computer Science  
A method, called Modal Resolution and inspired by Robinson's resolution method for classical logics, is presented for the system K and then extended to Q, T, S4, epistemic logic, and S5.  ...  This paper concerns the question of automated deduction methods for modal logic.  ...  Acknowledgment We thank Yves Auffray and Jean Jacques Hebrard for many critical discussions on an earlier version of the paper.  ... 
doi:10.1016/0304-3975(89)90137-0 fatcat:rj4yb5xsynabxo33tzoagid32q

A Calculus for Automatic Verification of Petri Nets Based on Resolution and Dynamic Logics

Cláudia Nalon, Bruno Lopes, Gilles Dowek, Edward Hermann Haeusler
2015 Electronical Notes in Theoretical Computer Science  
Dynamic Logics (DL) are a family of modal logics where each modality corresponds to a program.  ...  This works presents a resolution-based method for Petri-PDL, a DL where programs are replaced by Petri Nets.  ...  (PL), (K), and (Du), together with the inference rules (Sub), (MP), and (GEN), correspond to the usual axiomatisation for normal modal logics.  ... 
doi:10.1016/j.entcs.2015.04.008 fatcat:4idtel3ejfhorpeuca4jkpuyqm

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

Renate A. Schmidt, Ullrich Hustadt
2003 Lecture Notes in Computer Science  
We review and discuss the development of decision procedures for decidable extended modal logics and look at methods for automatically generating models.  ...  resolution.  ...  We also thank the reviewer for helpful comments.  ... 
doi:10.1007/978-3-540-24615-2_3 fatcat:jypyr3tokzhh7erjlyu5faipsi

Optimised Functional Translation and Resolution [chapter]

Ullrich Hustadt, Renate A. Schmidt, Christoph Weidenbach
1998 Lecture Notes in Computer Science  
It maps normal propositional modal logics into a class of path logics.  ...  Path logics are clausal logics over the language of the monadic fragment of sorted first-order logic with a special binary function symbol for defining accessibility.  ...  While for the basic modal logic, the classes of non-provable formulae (in the second column) are not harder than the classes of provable formulae, we see a noticeable difference between kt dum n, kt poly  ... 
doi:10.1007/3-540-69778-0_9 fatcat:ebkd73humzfydhuqpjdglmrrce

A new methodology for developing deduction methods

Renate A. Schmidt
2009 Annals of Mathematics and Artificial Intelligence  
This paper explores the use of resolution as a meta-framework for developing various, different deduction calculi. In this work the focus is on developing deduction calculi for modal dynamic logics.  ...  The approach is based on the translation of reasoning problems in modal logic to first-order clausal form and using a suitable refinement of resolution to construct and mimic derivations of the desired  ...  I also thank the reviewers for valuable comments. The research has been supported by UK EPSRC grants EP/D056152/1 and EP/F068530/1.  ... 
doi:10.1007/s10472-009-9155-4 fatcat:2fn56jyucfgcpmy55bsmpyehhu

Simulation and Synthesis of Deduction Calculi

Renate A. Schmidt
2010 Electronical Notes in Theoretical Computer Science  
This paper gives an overview of two methods for automatically or semi-automatically generating deduction calculi from the semantic specification of a logic.  ...  One approach is based on simulating deduction approaches with techniques of automated reasoning and first-order resolution.  ...  This is illustrated in [24] for extensions of the basic modal logic K .  ... 
doi:10.1016/j.entcs.2010.04.016 fatcat:pl77knopnzbx7ggugkxqyo2xi4

A clausal resolution method for extended computation tree logic ECTL

Alexander Bolotov, Artie Basukoski
2006 Journal of Applied Logic  
, we define a clausal resolution technique for Extended Computation Tree Logic (ECTL).  ...  The key elements of the resolution method for ECTL, namely the clausal normal form, the concepts of step resolution and a temporal resolution, are introduced and justified with respect to this new framework  ...  Acknowledgements We would like to thank Michael Fisher, Clare Dixon and Mark Reynolds for useful discussions during the preliminary work on the paper, Renate Schmidt for valuable comments on the relevant  ... 
doi:10.1016/j.jal.2005.06.003 fatcat:ydw6g3sbovegbcfd5hxmdcxhmi

Resolution-based methods for modal logics

H de Nivelle
2000 Logic Journal of the IGPL  
We concentrate on translation-based resolution methods for modal logics.  ...  In this paper we give an overview of resolution methods for extended propositional modal logics.  ...  Acknowledgements We thank the referees for valuable and detailed comments.  ... 
doi:10.1093/jigpal/8.3.265 fatcat:j3qr537gnzhbtljpsnerdrvasa

Page 3136 of Mathematical Reviews Vol. , Issue 95f [page]

1995 Mathematical Reviews  
Summary: “We present a resolution method for a nonmonotonic multimodal logic called hypothesis theory. As we define a reso- lution method, we need modal formulas to be in clausal normal form.  ...  But an important problem with modal logic is that there is no such simple normal form as in classical logic. So we propose an original clausal transformation for modal formulas.  ... 

Page 4445 of Mathematical Reviews Vol. , Issue 99g [page]

1999 Mathematical Reviews  
The presented resolution rules are split into four groups: initial resolution, modal resolution, step resolution, and temporal resolution.  ...  In the second part the author introduces the idea of a modal logic of agency. He goes on to discuss Pérn’s modal logic of agency, Brown’s logic of ability, and Belnap’s STIT-theory.  ... 

Forthcoming Papers

2002 Journal of Logic and Computation  
While this normal form was developed for use with execution and clausal resolution in temporal logics, we here show how it can represent, syntactically, -automata in a high-level way.  ...  We consider the relationship between -automata and a specific logical formulation based on a normal form for temporal logic formulae.  ...  While this normal form was developed for use with execution and clausal resolution in temporal logics, we here show how it can represent, syntactically, -automata in a high-level way.  ... 
doi:10.1093/logcom/12.3.545 fatcat:76u554iwwrbanemi5acreoed6e
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