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Hyperresolution for guarded formulae
 J. Symbolic Computat
, 2000
"... Abstract. This paper investigates the use of hyperresolution as a decision procedure and model builder for guarded formulae. In general hyperresolution is not a decision procedure for the entire guarded fragment. However we show that there are natural fragments which can be decided by hyperresolutio ..."
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Cited by 15 (9 self)
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Abstract. This paper investigates the use of hyperresolution as a decision procedure and model builder for guarded formulae. In general hyperresolution is not a decision procedure for the entire guarded fragment. However we show that there are natural fragments which can be decided by hyperresolution. In particular, we prove decidability of hyperresolution with or without splitting for the fragment GF1 − and point out several ways of extending this fragment without loosing decidability. As hyperresolution is closely related to various tableaux methods the present work is also relevant for tableaux methods. We compare our approach to hypertableaux, and mention the relationship to other clausal classes which are decidable by hyperresolution. 1
A Resolution Decision Procedure for Fluted Logic
 In Proc. CADE17
, 2000
"... Fluted logic is a fragment of firstorder logic without function symbols in which the arguments of atomic subformulae form ordered sequences. A consequence of this restriction is that, whereas firstorder logic is only semidecidable, fluted logic is decidable. In this paper we present a sound, comp ..."
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Cited by 12 (9 self)
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Fluted logic is a fragment of firstorder logic without function symbols in which the arguments of atomic subformulae form ordered sequences. A consequence of this restriction is that, whereas firstorder logic is only semidecidable, fluted logic is decidable. In this paper we present a sound, complete and terminating inference procedure for fluted logic. Our characterisation of fluted logic is in terms of a new class of socalled fluted clauses. We show that this class is decidable by an ordering refinement of firstorder resolution and a new form of dynamic renaming, called separation.
Computational Space Efficiency and Minimal Model Generation for Guarded Formulae
, 2001
"... This paper describes two hyperresolutionbased decision procedures for a subfragment of the guarded fragment. The rst procedure is a polynomial space decision procedure which eectively corresponds to polynomial space tableauxbased algorithms without blocking. The second procedure is a minimal mo ..."
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Cited by 7 (6 self)
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This paper describes two hyperresolutionbased decision procedures for a subfragment of the guarded fragment. The rst procedure is a polynomial space decision procedure which eectively corresponds to polynomial space tableauxbased algorithms without blocking. The second procedure is a minimal model generation procedure which constructs all and only minimal Herbrand models for guarded formulae. This procedure is based on hyperresolution, complement splitting and a model constraint propagation rule. Both procedures have concrete application domains and are relevant for all multimodal and description logics that can be embedded into the guarded fragment.
On the Universal Theory of Varieties of Distributive Lattices with Operators: Some Decidability and Complexity Results
 Proceedings of CADE16, LNAI 1632
, 1999
"... . In this paper we establish a link between satisability of universal sentences with respect to varieties of distributive lattices with operators and satisability with respect to certain classes of relational structures. We use these results for giving a method for translation to clause form of ..."
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Cited by 5 (3 self)
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. In this paper we establish a link between satisability of universal sentences with respect to varieties of distributive lattices with operators and satisability with respect to certain classes of relational structures. We use these results for giving a method for translation to clause form of universal sentences in such varieties, and then use results from automated theorem proving to obtain decidability and complexity results for the universal theory of some such varieties. 1 Introduction In this paper we give a method for automated theorem proving in the universal theory of certain varieties of distributive lattices with wellbehaved operators. For this purpose, we use extensions of Priestley's representation theorem for distributive lattices. The advantage of our method is that we avoid the explicit use of the full algebraic structure of such lattices, instead using sets endowed with a reexive and transitive relation and with additional functions and relations that corr...
Model Building with Ordered Resolution
 International Workshop on First Order Theorem Proving FTP'2000
, 2000
"... this paper, we propose to use clause sets to represent models. This idea is very simple and allows to combine in a well balanced way, expressive power with the \good" required properties of a reasonable model representation. Obviously, in order that the set of clauses specifying the model brings new ..."
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Cited by 4 (1 self)
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this paper, we propose to use clause sets to represent models. This idea is very simple and allows to combine in a well balanced way, expressive power with the \good" required properties of a reasonable model representation. Obviously, in order that the set of clauses specifying the model brings new information w.r.t. the initial one, a basic requirement is that these clause sets must have exactly one Herbrand model (on a given signature). Such clause sets are straightforward representations of their Herbrand models
Cancellative Superposition Decides the Theory of Divisible TorsionFree Abelian Groups
, 1999
"... In divisible torsionfree abelian groups, the eciency of the cancellative superposition calculus can be greatly increased by combining it with a variable elimination algorithm that transforms every clause into an equivalent clause without unshielded variables. We show that the resulting calculus is ..."
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Cited by 2 (0 self)
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In divisible torsionfree abelian groups, the eciency of the cancellative superposition calculus can be greatly increased by combining it with a variable elimination algorithm that transforms every clause into an equivalent clause without unshielded variables. We show that the resulting calculus is a decision procedure for the theory of divisible torsionfree abelian groups. Keywords Automated Theorem Proving, FirstOrder Logic, Superposition, Cancellative Abelian Monoids, Associativity, Commutativity, Variable Elimination, Term Rewriting, Divisible Torsionfree Abelian Groups, Decision Problem. 1 Introduction Equational reasoning in the presence of the associativity and commutativity axioms is known to be dicult { theoretically [4, 8], as well as practically [1, 9, 10, 11, 12, 13, 17]. Using ACunication and extended clauses the worst ineciencies of a nave approach can be avoided, but still the extended clauses lead to numerous variable overlaps { one of the most prolic types ...