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New Techniques in Clausal Form Generation

Giles Reger, Martin Suda, Andrei Voronkov
unpublished
This paper introduces a new top-down approach to clausal form generation for first-order formulas that aims to achieve this goal in a new way.  ...  In automated reasoning it is common that first-order formulas need to be translated into clausal normal form for proof search.  ...  Previous Work on Clausal Form Generation We review existing work on clausal form generation.  ... 
doi:10.29007/dzfz fatcat:wqki6n5fcraarhmkdoxgi7fu4i

EPiC Series in Computing New Techniques in Clausal Form Generation

Giles Reger, Martin Suda, Andrei Voronkov
2016 Pages 11-23 GCAI 2016. 2nd Global Conference on Artificial Intelligence   unpublished
This paper introduces a new top-down approach to clausal form generation for first-order formulas that aims to achieve this goal in a new way.  ...  In automated reasoning it is common that first-order formulas need to be translated into clausal normal form for proof search.  ...  Previous Work on Clausal Form Generation We review existing work on clausal form generation.  ... 
fatcat:vczpbcrhnbb3tccaz2euajoc7m

Sets with Cardinality Constraints in Satisfiability Modulo Theories [chapter]

Philippe Suter, Robin Steiger, Viktor Kuncak
2011 Lecture Notes in Computer Science  
formulas in negation normal form first described in [19, 21] .  ...  Conversion to negation normal form preserves the size and structure of the input formula and does not introduce new variables.  ...  Chapter 3 examines techniques first introduced in [19, 21] for reasoning on non-clausal constraints and shows how they can be used to extend the general DPLL(T ) scheme to form the new NC(T ) scheme.  ... 
doi:10.1007/978-3-642-18275-4_28 fatcat:kohimod67vc6fefogtu6klxka4

A Non-clausal Connection Calculus [chapter]

Jens Otten
2011 Lecture Notes in Computer Science  
A non-clausal connection calculus for classical first-order logic is presented that does not require the translation of input formulae into any clausal form.  ...  Copying of appropriate (sub-)clauses in a dynamic way, i.e. during the actual proof search, is realized by a generalized extension rule.  ...  The clausal connection calculus works for first-order formulae in disjunctive normal form or clausal form. Formulae that are not in this form have to be translated into clausal form.  ... 
doi:10.1007/978-3-642-22119-4_18 fatcat:n5o5knrq7nbvjeufz4bd5ezw6i

nanoCoP: A Non-clausal Connection Prover [chapter]

Jens Otten
2016 Lecture Notes in Computer Science  
Most of the popular efficient proof search calculi work on formulae that are in clausal form, i.e. in disjunctive or conjunctive normal form.  ...  Translating a proof in clausal form back into a more readable non-clausal proof of the original formula is not straightforward.  ...  The author would like to thank Wolfgang Bibel for his helpful comments on a preliminary version of this paper. nanoCoP: A Non-clausal Connection Prover  ... 
doi:10.1007/978-3-319-40229-1_21 fatcat:rhrl3tvvnrhfhloiwuz245wuxu

Quantifier-Free Equational Logic and Prime Implicate Generation [chapter]

Mnacho Echenim, Nicolas Peltier, Sophie Tourret
2015 Lecture Notes in Computer Science  
An algorithm for generating prime implicates of sets of equational ground clauses is presented.  ...  The set of prime implicates of a clausal set can thus be obtained by saturation of this set.  ...  form and T be a clausal tree such that ∀D ∈ C(T ), C ∨ D is in normal form and ∀l ∈ D, C < π l.  ... 
doi:10.1007/978-3-319-21401-6_21 fatcat:fwa6cibfwfg55de5bq53y55ymi

nanoCoP: Natural Non-clausal Theorem Proving

Jens Otten
2017 Proceedings of the Twenty-Sixth International Joint Conference on Artificial Intelligence  
Translating a proof in clausal form back into a more readable non-clausal proof of the original formula is not straightforward.  ...  Most efficient fully automated theorem provers implement proof search calculi that require the input formula to be in a clausal form, i.e. disjunctive or conjunctive normal form.  ...  Formulae that are not in clausal form are translated into clausal form in a preprocessing step.  ... 
doi:10.24963/ijcai.2017/695 dblp:conf/ijcai/Otten17 fatcat:e7twk7ckbnhjvee46egwmol7km

Curried least general generalization: A framework for higher order concept learning [chapter]

Srinivas Padmanabhuni, Randy Goebel, Koichi Furukawa
1998 Lecture Notes in Computer Science  
The idea is that the formal difficulties with the reasoning complexity of a higher order language can be controlled by forming new hypothetical terms restricted to those obtainable by Currying.  ...  Continued progress with research in inductive logic programming relies on further extensions of their underlying logics.  ...  The idea is that the formal difficulties with the reasoning complexity of a higher order language can be controlled by forming new hypothetical terms restricted to those obtainable by Currying.  ... 
doi:10.1007/3-540-64413-x_27 fatcat:hufdlwiejzhjrfer2cjzsd3aqy

Verifying Refutations with Extended Resolution [chapter]

Marijn J. H. Heule, Warren A. Hunt, Nathan Wetzler
2013 Lecture Notes in Computer Science  
We show how existing preprocessors and solvers can be modified to generate proofs in our new format.  ...  Our new format was designed with three goals: proofs should be easy to generate, proofs should be compact, and validating proofs must be simple.  ...  To overcome these problems, we propose a new clausal-proof format to compactly express techniques that go beyond resolution.  ... 
doi:10.1007/978-3-642-38574-2_24 fatcat:a5qzpf6upjcuxbbtnxqvk3tqwa

Heuristic Inverse Subsumption in Full-Clausal Theories [chapter]

Yoshitaka Yamamoto, Katsumi Inoue, Koji Iwanuma
2013 Lecture Notes in Computer Science  
Recently, it has been shown that IE can be logically reduced into a new form of IS, provided that it ensures the completeness of IE.  ...  Those BG techniques are originally used only for finding hypotheses in Horn clauses. In turn, they are extended so as to be applicable for finding hypotheses in full-clausal theories.  ... 
doi:10.1007/978-3-642-38812-5_17 fatcat:afxy2267gvgehfu6xkfzba2iwu

Applying GSAT to Non-Clausal Formulas [article]

R. Sebastiani
1994 arXiv   pre-print
In this paper we describe how to modify GSAT so that it can be applied to non-clausal formulas.  ...  Its value is computed in linear time, without constructing the CNF conversion itself. The proposed methodology applies to most of the variants of GSAT proposed so far.  ...  clausal form.  ... 
arXiv:cs/9406102v1 fatcat:pgtsofnfozgo7abpn7k7zjw2km

Unit Propagation in a Tableau Framework [chapter]

Gernot Stenz
2005 Lecture Notes in Computer Science  
Unit propagation is one of the most important techniques of efficient SAT solvers. Unfortunately, this technique is not directly applicable to first-order clausal tableaux.  ...  the usefulness of our new method.  ...  Conclusion In this paper we described the adaptation of the unit propagation SAT technique to a clausal tableau framework and the successful integration of this technique into the DCTP theorem prover.  ... 
doi:10.1007/11554554_29 fatcat:6iatu6544bfybgudfxffvx33zq

Applying GSATto Non-Clausal Formulas

R. Sebastiani
1994 The Journal of Artificial Intelligence Research  
In this paper we describe how to modify GSAT so that it can be applied to non-clausal formulas.  ...  Its value is computed in linear time, without constructing the CNF conversion itself. The proposed methodology applies to most of the variants of GSAT proposed so far.  ...  clausal form.  ... 
doi:10.1613/jair.49 fatcat:blitekyuhza7ziwanv6gpx6fui

Comparison of Upward and Downward Generalizations in CF-Induction [chapter]

Yoshitaka Yamamoto, Katsumi Inoue, Koji Iwanuma
2012 Lecture Notes in Computer Science  
CF-induction is a sound and complete procedure for finding hypotheses in full clausal theories.  ...  There are two possible ways to realize the generalization task in CF-induction.  ...  A clausal theory S is often identified with the conjunction of its clauses and is said to be in Conjunctive Normal Form (CNF). Let C and D be two clauses.  ... 
doi:10.1007/978-3-642-31951-8_31 fatcat:d3i7tqbybjapbhllwmryzwmzii

Fuzzy Maximum Satisfiability [article]

Mohamed El Halaby, Areeg Abdalla
2016 arXiv   pre-print
In this paper, we extend the Maximum Satisfiability (MaxSAT) problem to {\L}ukasiewicz logic.  ...  Three possible solutions (encodings) are proposed to the new problem: (1) Disjunctive Linear Relations (DLRs), (2) Mixed Integer Linear Programming (MILP) and (3) Weighted Constraint Satisfaction Problem  ...  It has been shown [7] that the satisfiability problem for any simple L-clausal form is solvable in linear time, contrary to the SAT problem in Boolean logic which is NP-complete in the general case.  ... 
arXiv:1602.02211v1 fatcat:una3l47hancfxm3kjl5ntemyia
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