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What you always wanted to know about rigid E-unification [chapter]

Anatoli Degtyarev, Andrei Voronkov
1996 Lecture Notes in Computer Science  
Our approach is applicable to the connection method and the tableau method and illustrated on the tableau method.  ...  The use of rigid E-uni cation and simultaneous rigid E-uni cation for such methods has been proposed by Gallier, Raatz and Snyder 36].  ...  this section connects two calculi: (i) calculus BSE of rigid equations; and (ii) tableau expansion rules for tableaux.  ... 
doi:10.1007/3-540-61630-6_4 fatcat:4vg333by65ew7lmsrjyssduqae

A Tableau Calculus for Minimal Modal Model Generation

Fabio Papacchini, Renate A. Schmidt
2011 Electronical Notes in Theoretical Computer Science  
In this paper we introduce a minimal model generation calculus for multi-modal logic K (m) and extensions of K (m) with the axioms T and B.  ...  A novelty of the calculus is a non-standard complement splitting rule designed for minimal model generation. Experiments show the rule has the added benefit of reducing the search space.  ...  It may be thought of as the simultaneous application of closure rules (for labelled formulae and labelled relations) and the box rule in standard multi-modal tableau calculi.  ... 
doi:10.1016/j.entcs.2011.10.013 fatcat:buviawlqbfhs5j5kuw3wakkhxu

leanTAP: Lean tableau-based deduction

Bernhard Beckert, Joachim Posegga
1995 Journal of automated reasoning  
The second is that we show how to optimize the NNF without extra cost by changing the sequence of disjunctively connected formulae.  ...  are implicitly disjunctively connected, and the formulae on a branch are implicitly conjunctively connected.  ... 
doi:10.1007/bf00881804 fatcat:jaksyjva4nbwnkxl6bpvefclpq

De Finettian Logics of Indicative Conditionals Part II: Proof Theory and Algebraic Semantics

Paul Égré, Lorenzo Rossi, Jan Sprenger
2021 Journal of Philosophical Logic  
Here we provide the proof theory for the resulting logics and , using tableau calculi and sequent calculi, and proving soundness and completeness results.  ...  1935, 1944) on the one hand, and by Cooper (Inquiry, 11, 295–320, 1968) and Cantwell (Notre Dame Journal of Formal Logic, 49, 245–260, 2008) on the other.  ...  We give a discussion of that result and compare both logics in Section 5. Tableau Calculi In this section, we introduce sound and complete tableau calculi for CC/TT and DF/TT.  ... 
doi:10.1007/s10992-020-09572-7 fatcat:7mikxvsvqbhdhoqplpzqc3s7dy

Incremental variable splitting

Christian Mahesh Hansen, Roger Antonsen, Martin Giese, Arild Waaler
2012 Journal of symbolic computation  
The variable splitting method for free-variable tableau calculi provides an admissibility condition under which the same free variables can be assigned values independently on different branches.  ...  While this has a large potential for automated proof search, a direct implementation of this condition is impractical.  ...  Since it is impractical to check for the existence of a closing substitution for the whole tableau every time a new connection is introduced, 9 proof search procedures usually close branches one by one  ... 
doi:10.1016/j.jsc.2011.12.032 fatcat:lfg7pe643zdwvghvkhel334v4u

Incremental Closure of Free Variable Tableaux [chapter]

Martin Giese
2001 Lecture Notes in Computer Science  
Incremental Closure is a way of organizing the search for closing instantiations that avoids this inefficiency.  ...  If the correct instantiation is hard to find, this can lead to a significant amount of duplicated work.  ...  Acknowledgments I thank Wolfgang Ahrendt, Elmar Habermalz, Reiner Hähnle and the anonymous referees for their numerous and helpful comments on drafts of this paper.  ... 
doi:10.1007/3-540-45744-5_46 fatcat:iymsbye2lfcofoe5lzlya7vlhy

Superposition-based Equality Handling for Analytic Tableaux

Martin Giese
2006 Journal of automated reasoning  
We prove completeness of this calculus by an adaptation of the model generation technique commonly used for completeness proofs of superposition in the context of resolution calculi.  ...  We present a variant of the basic ordered superposition rules to handle equality in an analytic free-variable tableau calculus.  ...  I also thank Bernhard Beckert, Reiner Hähnle, and Peter Schmitt for many fruitful discussions and good advice, leading to the results presented in this article.  ... 
doi:10.1007/s10817-006-9050-1 fatcat:xkdw4f2bdfbabe346iomeaorbe

Automated Synthesis of Tableau Calculi

Renate Schmidt, Dmitry Tishkovsky, Martin Giese
2011 Logical Methods in Computer Science  
This paper presents a method for synthesising sound and complete tableau calculi.  ...  Given a specification of the formal semantics of a logic, the method generates a set of tableau inference rules that can then be used to reason within the logic.  ...  This means that the synthesised tableau calculi can be used for finding models.  ... 
doi:10.2168/lmcs-7(2:6)2011 fatcat:wcvr7oon3ncjlniwxvvpd436mi

'Living Book' :- 'Deduction', 'Slicing', 'Interaction' [chapter]

Peter Baumgartner, Ulrich Furbach, Margret Gross-Hardt, Alex Sinner
2003 Lecture Notes in Computer Science  
The computation of such assemblies is carried out by a model-generating theorem prover for first-order logic with a default negation principle.  ...  This paper describes the Living Book and the use of theorem proving technology as a core component in the knowledge management system (KMS) of the Living Book.  ...  Hyper tableau calculi are tableau calculi in the tradition of SATCHMO [28] .  ... 
doi:10.1007/978-3-540-45085-6_23 fatcat:jyjaaobhvne7vgxte4agfh2j7e

Incremental theory reasoning methods for semantic tableaux [chapter]

Bernhard Beckert, Christian Pape
1996 Lecture Notes in Computer Science  
In this paper we present incremental theory reasoning, a method that improves the interaction between the foreground reasoner and the background theory reasoner and, thus, the e ciency of the combined  ...  The use of incremental theory reasoning in free variable semantic tableaux and the cost reduction that can be achieved are discussed; as an example, completion-based equality reasoning is presented, including  ...  of a tableau are implicitly disjunctively connected and the formulae on a branch are implicitly conjunctively connected.  ... 
doi:10.1007/3-540-61208-4_7 fatcat:tq6dxnr6pvcfpjvaizksqrew6e

Fair Constraint Merging Tableaux in Lazy Functional Programming Style [chapter]

Reiner Hähnle, Niklas Sörensson
2003 Lecture Notes in Computer Science  
This avoids backtracking as necessary in destructive first order free variable tableaux. The first sound and complete implementation of this paradigm was given in an object-oriented style by Giese.  ...  Constraint merging tableaux maintain a system of all closing substitutions of all subtableau up to a certain depth, which is incrementally increased.  ...  When we write "free variable" we mean it in the sense of tableau proofs.  ... 
doi:10.1007/978-3-540-45206-5_21 fatcat:n5ax4rc4gzedjf5xe45fcai2bq

Toward an Efficient Equality Computation in Connection Tableaux: A Modification Method without Symmetry Transformation

Koji Iwanuma, Hidetomo Nabeshima, Katsumi Inoue
2009 International Workshops on First Order Theorem Proving  
The symmetry elimination may produce an exponential number of clauses from a given single clause, which inevitably causes a huge amount of redundant backtracking in connection tableaux.  ...  In this paper, we study an efficient equality computation in connection tableaux, and give a new variant of Brand, Bachmair-Ganzinger-Voronkov and Paskevich's modification methods, where the symmetry elimination  ...  The right tableau in Fig. 1 succeeded in being closed, and simultaneously satisfies the ordering constraints.  ... 
dblp:conf/ftp/IwanumaNI09 fatcat:ejq246suvzhpbikseyirpta2iu

Tableaux for Reasoning about Atomic Updates [chapter]

Christian G. Fermüller, Georg Moser, Richard Zach
2001 Lecture Notes in Computer Science  
These logics are studied also in a many-valued context. Adequate tableau calculi are given.  ...  A state α of a database is an atomic update of a state β if at most one atomic statement is evaluated differently in α compared to β.  ...  By an integrity constraint we simply mean a condition, referring to specific atoms and/or schematic variables, that has to be fulfilled in all states of a given database.  ... 
doi:10.1007/3-540-45653-8_44 fatcat:4ihvmph4hfewlfhmrjqywouona

Equality Preprocessing in Connection Calculi

Benjamin E. Oliver, Jens Otten
2020 Conference on Automated Deduction  
We present an extensible system for equality preprocessing in connection calculi (EPICC) that can be used as a tool in reducing the search space of problems that contain equality.  ...  We specify a number of preprocessing rules, describe an implementation of these rules and compare it with existing approaches for dealing with equality in connection calculi.  ...  Acknowledgments We would like to thank the reviewers of a previous version of this paper for their comments.  ... 
dblp:conf/cade/OliverO20 fatcat:ai5dfuvn6zfbfhg5dnieuj6q7q

Computing answers with model elimination

Peter Baumgartner, Ulrich Furbach, Frieder Stolzenburg
1997 Artificial Intelligence  
The presented calculi can also be used successfully in the context of automated theorem proving.  ...  In first-order automatic theorem proving one is interested in the question whether a given formula follows logically from a set of axioms.  ...  This means that one of the inequality constraints stated in the definition of blockwise regularity is violated.  ... 
doi:10.1016/s0004-3702(96)00042-2 fatcat:otkffi2y7bdizhl2kx3ssiogze
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