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Redundancy in logic I: CNF propositional formulae

Paolo Liberatore
2005 Artificial Intelligence  
We study the problem of checking whether a CNF formula (a set of clauses) is redundant, that is, it contains clauses that can be derived from the other ones.  ...  Any CNF formula can be made irredundant by deleting some of its clauses: what results is an irredundant equivalent subset (I.E.S.)  ...  Acknowledgements Many thanks to Pierre Marquis for suggesting the problem of redundancy, to Marco Schaerf for his comments on a previous version of this paper, and to the anonymous reviewers for their  ... 
doi:10.1016/j.artint.2004.11.002 fatcat:otffil2435fi3k7srpbpfunzji

On some bandwidth restricted versions of the satisfiability problem of propositional CNF formulas

V. Arvind, S. Biswas
1989 Theoretical Computer Science  
In the present paper we study the complexity of some restricted versions of the satisfiability problem for propositional CNF formulas.  ...  We define these restrictions through their corresponding languages which are identified using the self-reducibility property of satisfiable propositional CNF formulas.  ...  Concluding remarks The NP-completeness proofs for L2 and L, use Borger's simulation of Turing machine computations through propositional formulas in CNF.  ... 
doi:10.1016/0304-3975(89)90125-4 fatcat:tun2tknzbrbgzhokgfqdarpv6y

Generalizing Redundancy in Propositional Logic: Foundations and Hitting Sets Duality [article]

Anton Belov, Joao Marques-Silva
2012 arXiv   pre-print
Detection and elimination of redundant clauses from propositional formulas in Conjunctive Normal Form (CNF) is a fundamental problem with numerous application domains, including AI, and has been the subject  ...  In this report we present a generalized theoretical framework of labelled CNF formulas that unifies various extensions of the redundancy detection and removal problem and allows to derive a number of results  ...  Conclusion This report presents a framework of labelled CNF formulas that allows to generalize and extend the existing work on redundancy detection and removal in CNF formulas.  ... 
arXiv:1207.1257v2 fatcat:rwb2ncoqnjen3atm5ltjiwiieu

Redundancy in Logic III: Non-Mononotonic Reasoning [article]

Paolo Liberatore
2005 arXiv   pre-print
Results about the redundancy of circumscriptive and default theories are presented. In particular, the complexity of establishing whether a given theory is redundant is establihsed.  ...  All formulae considered in this paper are propositional and finite Boolean formulae over a finite alphabet. We typically use formulae in CNF, that is, sets of clauses.  ...  A clause is (classically) redundant in a CNF formula Π if Π\{γ} |= γ. A CNF formula is (classically) redundant if it is equivalent to one of its proper subsets.  ... 
arXiv:cs/0507048v2 fatcat:negvhypo5fgm7k6kedxhr6z3n4

Redundancy in Logic II: 2CNF and Horn Propositional Formulae [article]

Paolo Liberatore
2005 arXiv   pre-print
We report complexity results about redundancy of formulae in 2CNF form. We first consider the problem of checking redundancy and show some algorithms that are slightly better than the trivial one.  ...  Some results about Horn formulae are also shown.  ...  Introduction The complexity of some problems related to the redundancy of propositional CNF formulae has been studied in a previous paper [Lib05] .  ... 
arXiv:cs/0506074v3 fatcat:j46ccbnoj5eixe7uqkcqaha4gm

Redundancy in logic III: Non-monotonic reasoning

Paolo Liberatore
2008 Artificial Intelligence  
If a CNF formula contains a redundant clause, it is redundant (equivalent to one of its proper subsets); the converse is true in propositional logic, but not in all logics.  ...  Both circumscription and default logic differ from classical propositional logic. This difference affects redundancy.  ...  This is the corresponding of Lemma 4 of the article about redundancy of propositional CNF formulae [26] , which has been useful because it allows to "localize" problems about redundancy.  ... 
doi:10.1016/j.artint.2008.02.003 fatcat:faejhx352va2pi5gemiyt5rwby

Extended ASP Tableaux and rule redundancy in normal logic programs

MATTI JÄRVISALO, EMILIA OIKARINEN
2008 Theory and Practice of Logic Programming  
InProceedings of the 22nd International Conference on Logic Programming (ICLP 2006), S. Etalle and M. Truszczynski, Eds. Lecture Notes in Computer Science, vol. 4079.  ...  Closely related to Extended ASP Tableaux, we empirically investigate the effect of redundant rules on the efficiency of ASP solving.  ...  Financial support from Academy of Finland (grant #211025), Helsinki Graduate School in Computer Science and Engineering, Emil Aaltonen Foundation, the Finnish Cultural Foundation (EO), the Technological  ... 
doi:10.1017/s1471068408003578 fatcat:fdqwcjviqzaiplpjpt2egippqa

Redundancy in logic II: 2CNF and Horn propositional formulae

Paolo Liberatore
2008 Artificial Intelligence  
We report results about the redundancy of formulae in 2CNF form.  ...  In particular, we give a slight improvement over the trivial redundancy algorithm and give some complexity results about some problems related to finding Irredundant Equivalent Subsets (I.E.S.) of 2CNF  ...  Liberatore [18] investigated redundancy for some non-classical logics. Related work regarding propositional logic can be roughly divided into three classes.  ... 
doi:10.1016/j.artint.2007.06.003 fatcat:rxgiyj65gvbnpautp6zax6w2ve

Computing Minimal Sets on Propositional Formulae I: Problems & Reductions [article]

Joao Marques-Silva, Mikolas Janota
2014 arXiv   pre-print
Progress in SAT solving algorithms has motivated an ever increasing number of practical applications in recent years.  ...  This paper addresses a number of representative function problems defined on Boolean formulas, and shows that all these function problems can be reduced to a generic problem of computing a minimal set  ...  Propositional Formulae Standard propositional logic definitions are used throughout the paper (e.g. [48, 10] ), some of which are reviewed in this section.  ... 
arXiv:1402.3011v2 fatcat:ia3domcftjdyhjjzjpq2lnqwru

Quantifier Elimination With Structural Learning [article]

Eugene Goldberg
2018 arXiv   pre-print
We consider the Quantifier Elimination (QE) problem for propositional CNF formulas with existential quantifiers. QE plays a key role in formal verification.  ...  Redundancy of a clause is a structural property (i.e. it holds only for a subset of logically equivalent formulas as opposed to a semantic property).  ...  That is the fact that clause C is redundant in formula F may not hold in a formula F ′ logically equivalent to F .  ... 
arXiv:1810.00160v3 fatcat:sshmjcajn5aphesdn2uxhnjvyi

An analysis of empirical testing for modal decision procedures

I Horrocks
2000 Logic Journal of the IGPL  
However, the very effectiveness of the new systems has revealed serious weaknesses in existing empirical test suites and methodologies.  ...  As both computational complexity and algorithm complexity are generally unchanged, neither is useful in analysing and comparing these new systems and their various optimisations.  ...  , each time applying to sub-formulae the propositional CNF conversion and the transformation 2r V j W i ϕ ij =⇒ V j 2r W i ϕ ij . way of converting any modal formula into 3CNF 2m .  ... 
doi:10.1093/jigpal/8.3.293 fatcat:bf5kfnx35fh3hhmtxoncxitise

On Computing Minimal Equivalent Subformulas [chapter]

Anton Belov, Mikoláš Janota, Inês Lynce, Joao Marques-Silva
2012 Lecture Notes in Computer Science  
A propositional formula in Conjunctive Normal Form (CNF) may contain redundant clauses -clauses whose removal from the formula does not affect the set of its models.  ...  A formula obtained by the removal of all redundant clauses from a given CNF formula F is called a Minimal Equivalent Subformula (MES) of F.  ...  Besides propositional logic formulas, the problem of the identification of redundant constraints is relevant in other domains.  ... 
doi:10.1007/978-3-642-33558-7_14 fatcat:yjmbaawrjrbs5mbpyd2g6hcx2q

Optimal Axiomatizations of Finitely Valued Logics

Gernot Salzer
2000 Information and Computation  
We show that the problem can be viewed as the minimization of certain propositional formulas.  ...  We investigate the problem of finding optimal axiomatizations for operators and distribution quantifiers in finitely valued first-order logics.  ...  ACKNOWLEDGMENTS I thank Matthias Baaz and Richard Zach for enlightening discussions on this topic.  ... 
doi:10.1006/inco.1999.2862 fatcat:r6r7p6dturbbtnfrmnlyugw53u

Let the Solver Deal with Redundancy

Cédric Piette
2008 2008 20th IEEE International Conference on Tools with Artificial Intelligence  
Dealing with redundancy in CNF formulae while preserving the performance of SAT solvers is clearly an important challenge.  ...  Handling redundancy in propositional reasoning and search is an active path of theoretical research.  ...  About redundancy in CNF formulae Let L be a standard Boolean (also called propositional) logical language built on a finite set of Boolean variables.  ... 
doi:10.1109/ictai.2008.38 dblp:conf/ictai/Piette08 fatcat:bu5iguxurjcyzkxagfobujsmhm

Blocked Clauses in First-Order Logic [article]

Benjamin Kiesl, Martin Suda, Martina Seidl, Hans Tompits, Armin Biere
2017 arXiv   pre-print
Their definition, which relies on a simple syntactic criterion, guarantees that they are both redundant and easy to find. In this paper, we lift the notion of blocked clauses to first-order logic.  ...  We introduce two types of blocked clauses, one for first-order logic with equality and the other for first-order logic without equality, and prove their redundancy.  ...  In propositional logic, a clause C is blocked by a literal L ∈ C in a CNF formula F if all binary resolvents of C upon L with clauses from F \{C} are tautologies.  ... 
arXiv:1702.00847v1 fatcat:kwzzzo36bvamdiqblrf3a2bhdq
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