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A resolution rule for well-formed formulae

K.S.H.S.R. Bhatta, Harish Karnick
1991 Theoretical Computer Science  
Karnick, A resohttion rule for well-formed formulae, Theoretical Computer Science 81 (1991) 223-235.  ...  A resolution proof procedure that operates on well-formed formulae with all quantifiers in place is presented.  ...  Thus, WFF-resolution has been proved to be sound and complete. m In this paper we have described a resolution proof rule for well-formed formulae with quantifiers in place and proved its soundness and  ... 
doi:10.1016/0304-3975(91)90192-5 fatcat:c3obmy2xqnbsvlkoheib5a7s6u

Clausal Resolution for CTL [chapter]

Alexander Bolotov, Clare Dixon, Michael Fisher
1999 Lecture Notes in Computer Science  
The key elements of the resolution method, namely the normal form, the concept of step resolution and a novel temporal resolution rule, are introduced, justified, and applied.  ...  Thus, here we extend our clausal resolution method for lineartime temporal logics to a branching-time framework, in particular to the powerful CTL* logic.  ...  The authors would like to thank the anonymous referees for useful comments. This work was supported by EPSRC under research grant GR/L87491.  ... 
doi:10.1007/3-540-48340-3_13 fatcat:24vae5qr4bgphhkg7q3tceepei

A Resolution Method for Temporal Logic

Michael Fisher
1991 International Joint Conference on Artificial Intelligence  
In this paper, a resolution method for propositional temporal logic is presented.  ...  Temporal formulae, incorporating both past-time and future-time temporal operators, are converted to Separated Normal Form (SNF), then both non-temporal and temporal resolution rules are applied.  ...  Finally, note that any well-formed formula in our logic can be translated to an equivalent set of rules in SNF.  ... 
dblp:conf/ijcai/Fisher91 fatcat:qu2vuk6jpzgjbn45xptweph3rq

A Note on Backward Dual Resolution and Its Application to Proving Completeness of Rule-Based Systems

Antoni Ligeza
1993 International Joint Conference on Artificial Intelligence  
The main idea of bd-resolution consists in proving validity of a formula in disjunctive normal form, by generating an empty tautology formula from it; it is shown that the initial formula is a logical  ...  In this paper, a method of theorem proving dual to resolution method is presented in brief. The investigated method is called backward dual resolution or bd-re solution, for short.  ...  First, instead of converting a formula to its clausal form one can transform the initial formula to a dual form, consisting of an alternative of conjunctions of literals.  ... 
dblp:conf/ijcai/Ligeza93 fatcat:mupv6j6wxzdvhghvptduwcrt3a

A normal form for first-order temporal formulae [chapter]

Michael Fisher
1992 Lecture Notes in Computer Science  
In this paper a normal form for formulae of a first-order temporal logic is described.  ...  This normal form, called First-Order Separated Normal Form (SNF ƒ ), forms the basis of both a temporal resolution method [5] and a family of executable temporal logics [2] .  ...  The satisfaction relation, | =, relates such tuples to well-formed formulae.  ... 
doi:10.1007/3-540-55602-8_178 fatcat:htbxjmpkjvgy5eafkcwbsnldyq

A Normal Form for Temporal Logics and its Applications in Theorem-Proving and Execution

MICHAEL FISHER
1997 Journal of Logic and Computation  
This normal form not only provides a simple and concise representation for temporal formulae, but is also used as the basis for both a resolution proof method and an execution mechanism for this type of  ...  In this paper a normal form, called Separated Normal Form (SNF), for temporal logic formulae is described.  ...  Acknowledgements The author wishes to thank Clare Dixon, Rajeev Goré, Rob Johnson, Brian Monahan, Philippe Noël, Richard Owens, Martin Peim, Mike Wooldridge and the two anonymous referees for their helpful  ... 
doi:10.1093/logcom/7.4.429 fatcat:nsicehhgsndmrffuq475ivz7pq

A Resolution Prover for Coalition Logic

Cláudia Nalon, Lan Zhang, Clare Dixon, Ullrich Hustadt
2014 Electronic Proceedings in Theoretical Computer Science  
The theorem prover CLProver is based on recent work on a resolution-based calculus for Coalition Logic that operates on coalition problems, a normal form for Coalition Logic.  ...  We present a prototype tool for automated reasoning for Coalition Logic, a non-normal modal logic that can be used for reasoning about cooperative agency.  ...  We denote by Σ ϕ , where Σ ϕ ⊆ Σ, the set of agents occurring in a well-formed formula ϕ. If Φ is a set of well-formed formulae, Σ Φ ⊆ Σ denotes ϕ∈Φ Σ ϕ .  ... 
doi:10.4204/eptcs.146.9 fatcat:rjwscxp7jbawvgbj7b35ux5g4i

Deciding Monodic Fragments by Temporal Resolution [chapter]

Ullrich Hustadt, Boris Konev, Renate A. Schmidt
2005 Lecture Notes in Computer Science  
For the first, we state a very general decidability result, which is independent of the particular decision procedure used to decide the first-order part of the logic.  ...  This allows us to transfer existing results on decidability by resolution for first-order fragments to monodic first-order temporal logic and obtain new decision procedures.  ...  together with an eventuality literal forms the premises for the ground and nonground eventuality resolution rules.  ... 
doi:10.1007/11532231_15 fatcat:wc3jt23qkvctffj3juroxe2unu

A resolution-based proof method for temporal logics of knowledge and belief [chapter]

Michael Fisher, Michael Wooldridge, Clare Dixon
1996 Lecture Notes in Computer Science  
First, a formula to be tested for unsatisfiability is translated into a normal form.  ...  Secondly, a family of resolution rules are used, to deal with the interactions between the various operators of the logics.  ...  Notation: If L is a logical language, then we write Form(L) for the set of (well-formed) formulae of L.  ... 
doi:10.1007/3-540-61313-7_72 fatcat:ut6czempxbcntdccrzcbc7dbhq

Monotonic semantic interpretation

Hiyan Alshawi, Richard Crouch
1992 Proceedings of the 30th annual meeting on Association for Computational Linguistics -  
The paper describes how monotonic reference resolution and scoping can be carried out using a revised Quasi Logical Form (QLF) representation.  ...  Semantics for QLF are presented in which the denotations of formulas are extended monotonically as QLF expressions are resolved.  ...  Two rules are applicable to form expressions, corresponding to the cases of an uninstantiated or instantiated resolution meta-variable: Q10 W(F,v) if W(F[R(P)/_r],v) where: F is a formula form(C,R,_r  ... 
doi:10.3115/981967.981972 dblp:conf/acl/AlshawiC92 fatcat:m4c23yss75gh7gwmpdf2pwzft4

On Sequent Systems and Resolution for QBFs [chapter]

Uwe Egly
2012 Lecture Notes in Computer Science  
We show that there are classes of formulas for which there are short cut-free tree proofs in a sequent system, but any Q-resolution refutation of the negation of the formula is exponential.  ...  Q-resolution is an elegant extension of propositional resolution to QBFs and is applicable to formulas in prenex conjunctive normal form.  ...  The Construction of ϕ n We start with a version of the well-known pigeon hole formula in disjunctive normal form.  ... 
doi:10.1007/978-3-642-31612-8_9 fatcat:yt6t6sqa5nd4piszchvyfi7l24

A Many-Sorted Calculus Based on Resolution and Paramodulation

Christoph Walther
1983 International Joint Conference on Artificial Intelligence  
The first-order calculus whose well formed formulas are clauses and whose sole inference rules are factorization, resolution and paramodulation is extended to a many-sorted calculus.  ...  As a basis for Automated Theorem Proving, this many-sorted calculus leads to a remarkable reduction of the search space and also to simpler proofs.  ...  inference rules of factorization, resolution and paramodulation. is a deduction without paramodulation and is a deduction without resolution. denotes the set of all ground Instances of the clauses in S  ... 
dblp:conf/ijcai/Walther83 fatcat:wfccfdf3ujfw3exejtl3cuv7xi

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.  ...  Conclusions The described transformation produces clauses of very simple form. Resolution method become much simpler.  ...  Well-known transformation methods of the formulas of classical logic are not suitable for neither modal nor hybrid logics. Transformation of formulas of hybrid logics needs a different approach.  ... 
doi:10.15388/lmr.2011.ml06 fatcat:mxlw5p6emfhhtll6hpgrtrehs4

Normal Forms and Proofs in Combined Modal and Temporal Logics [chapter]

U. Hustadt, C. Dixon, R. A. Schmidt, M. Fisher
2000 Lecture Notes in Computer Science  
This framework allows us to combine di erent normal forms, in particular, a separated normal form for temporal logic and a rst-order clausal form for modal logics.  ...  The calculus of the framework consists of temporal resolution rules and standard rst-order resolution rules.  ...  Let M be a connected interpretation and ' be a well-formed formula of MTL. Then M; (t 0 ; 0) j = 2 ' i M; w j = ' for every point w in M.  ... 
doi:10.1007/10720084_6 fatcat:5mfajnouajdpzkcuz6qcckc4ky

Non-clausal reasoning with propositional definite theories [chapter]

Zbigniew Stachniak
1998 Lecture Notes in Computer Science  
We argue that efficient automated reasoning techniques which utilize definite formula representation of knowledge (such as SLD-resolution) can be developed for classical and a variety of non-classical  ...  The notion of a definite formula is generic in the sense that it is available to any logical calculus.  ...  We have selected this particular logic since it is a well-known non-classical calculus (see [3] for its definition) and since a non-clausal resolution proof system for L 3 is available (cf.  ... 
doi:10.1007/bfb0055921 fatcat:onfhgujs2rcpffkwtpgmhe5k2m
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