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159
E  A Brainiac Theorem Prover
, 2002
"... We describe the superpositionbased theorem prover E. E is a sound and complete... ..."
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Cited by 128 (18 self)
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We describe the superpositionbased theorem prover E. E is a sound and complete...
Reducing SHIQ − Description Logic to Disjunctive Datalog Programs
, 2004
"... As applications of description logics proliferate, efficient reasoning with large ABoxes (sets of individuals with descriptions) becomes ever more important. Motivated by the prospects of reusing optimization techniques from deductive databases, in this paper, we present a novel approach to checking ..."
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Cited by 125 (19 self)
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As applications of description logics proliferate, efficient reasoning with large ABoxes (sets of individuals with descriptions) becomes ever more important. Motivated by the prospects of reusing optimization techniques from deductive databases, in this paper, we present a novel approach to checking consistency of ABoxes, instance checking and query answering, w.r.t. ontologies formulated using a slight restriction of the description logic SHIQ. Our approach proceeds in three steps: (i) the ontology is translated into firstorder clauses, (ii) TBox and RBox clauses are saturated using a resolutionbased decision procedure, and (iii) the saturated set of clauses is translated into a disjunctive datalog program. Thus, query answering can be performed using the resulting program, while applying all existing optimization techniques, such as joinorder optimizations or magic sets. Equally important, the resolutionbased decision procedure we present is for unary coding of numbers worstcase optimal, i.e. it runs in EXPTIME.
Lazy Satisfiability Modulo Theories
 Journal on Satisfiability, Boolean Modeling and Computation
, 2007
"... Satisfiability Modulo Theories (SMT) is the problem of deciding the satisfiability of a firstorder formula with respect to some decidable firstorder theory T (SMT (T)). These problems are typically not handled adequately by standard automated theorem provers. SMT is being recognized as increasingl ..."
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Cited by 79 (33 self)
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Satisfiability Modulo Theories (SMT) is the problem of deciding the satisfiability of a firstorder formula with respect to some decidable firstorder theory T (SMT (T)). These problems are typically not handled adequately by standard automated theorem provers. SMT is being recognized as increasingly important due to its applications in many domains in different communities, in particular in formal verification. An amount of papers with novel and very efficient techniques for SMT has been published in the last years, and some very efficient SMT tools are now available. Typical SMT (T) problems require testing the satisfiability of formulas which are Boolean combinations of atomic propositions and atomic expressions in T, so that heavy Boolean reasoning must be efficiently combined with expressive theoryspecific reasoning. The dominating approach to SMT (T), called lazy approach, is based on the integration of a SAT solver and of a decision procedure able to handle sets of atomic constraints in T (Tsolver), handling respectively the Boolean and the theoryspecific components of reasoning. Unfortunately, neither the problem of building an efficient SMT solver, nor even that of acquiring a comprehensive background knowledge in lazy SMT, is of simple solution. In this paper we present an extensive survey of SMT, with particular focus on the lazy approach. We survey, classify and analyze from a theoryindependent perspective the most effective techniques and optimizations which are of interest for lazy SMT and which have been proposed in various communities; we discuss their relative benefits and drawbacks; we provide some guidelines about their choice and usage; we also analyze the features for SAT solvers and Tsolvers which make them more suitable for an integration. The ultimate goals of this paper are to become a source of a common background knowledge and terminology for students and researchers in different areas, to provide a reference guide for developers of SMT tools, and to stimulate the crossfertilization of techniques and ideas among different communities.
Theorem Proving with Ordering and Equality Constrained Clauses
 Journal of Symbolic Computation
, 1995
"... constraint strategies and saturation Given a signature F , below we denote by S the set of all clauses built over F , and similarly by C the set of all constraints, and by EC the set of all equality constraints (which is a subset of C). Definition 3.1. An inference rule IR is a mapping of ntuples ..."
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Cited by 73 (19 self)
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constraint strategies and saturation Given a signature F , below we denote by S the set of all clauses built over F , and similarly by C the set of all constraints, and by EC the set of all equality constraints (which is a subset of C). Definition 3.1. An inference rule IR is a mapping of ntuples of clauses to sets of triples containing a clause, a constraint and an equality constraint: IR : S n \Gamma! P(hS; C; ECi) An inference system is a set of inference rules. Definition 3.2. A constraint inheritance strategy is a function mapping a clause, two constraints and an equality constraint to a clause and a constraint: H : S \Theta C \Theta C \Theta EC \Gamma! S \Theta C Inference systems and constraint inheritance strategies are combined to produce inferences in the usual sense: given constrained clauses C 1 [[T 1 ]]; : : : ; Cn [[T n ]], we obtain a conclusion C [[T ]] as follows. Applying an inference rule to C 1 ; : : : ; Cn we obtain a triple hD; OT;ET i. Then the constraint...
Basic Paramodulation
 Information and Computation
, 1995
"... We introduce a class of restrictions for the ordered paramodulation and superposition calculi (inspired by the basic strategy for narrowing), in which paramodulation inferences are forbidden at terms introduced by substitutions from previous inference steps. In addition we introduce restrictions bas ..."
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Cited by 67 (11 self)
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We introduce a class of restrictions for the ordered paramodulation and superposition calculi (inspired by the basic strategy for narrowing), in which paramodulation inferences are forbidden at terms introduced by substitutions from previous inference steps. In addition we introduce restrictions based on term selection rules and redex orderings, which are general criteria for delimiting the terms which are available for inferences. These refinements are compatible with standard ordering restrictions and are complete without paramodulation into variables or using functional reflexivity axioms. We prove refutational completeness in the context of deletion rules, such as simplification by rewriting (demodulation) and subsumption, and of techniques for eliminating redundant inferences.
Towards an Automatic Analysis of Security Protocols in FirstOrder Logic
, 1999
"... . The NeumanStubblebine key exchange protocol is formalized in rstorder logic and analyzed by the automated theorem prover Spass. In addition to the analysis, we develop the necessary theoretical background providing new (un)decidability results for monadic rstorder fragments involved in the a ..."
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Cited by 62 (4 self)
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. The NeumanStubblebine key exchange protocol is formalized in rstorder logic and analyzed by the automated theorem prover Spass. In addition to the analysis, we develop the necessary theoretical background providing new (un)decidability results for monadic rstorder fragments involved in the analysis. The approach is applicable to a variety of security protocols and we identify possible extensions leading to future directions of research. 1 Introduction The growing importance of the internet causes a growing need for security protocols that protect transactions and communication. It turns out that the design of such protocols is highly errorprone. Therefore, a variety of dierent methods have been described that analyze security protocols to discover aws. The topic of this paper is to add a further, new method that is based on automated theorem proving in rstorder logic. In the context of rstorder automated theorem proving, Schumann (1997) implemented the wellknown ...
SPASS FLOTTER Version 0.42
"... t represents the sort restrictions on the variables. There are two extra inference rules which transform the sort constraint into solved form: Sort resolution and empty sort. These rules 1 The name is the result of a lunch break, FLOTTER means "faster", in German. 2 Synergetic Prover Augmenting ..."
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Cited by 54 (3 self)
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t represents the sort restrictions on the variables. There are two extra inference rules which transform the sort constraint into solved form: Sort resolution and empty sort. These rules 1 The name is the result of a lunch break, FLOTTER means "faster", in German. 2 Synergetic Prover Augmenting Superposition with Sorts, SPASS means "fun", in German. implement a specific strategy of the sorted unification algorithm [15] on the sort constraint literals. In addition to these inference rules, SPASS includes a splitting rule. The splitting rule is a variant of the usual firule of tableau. If SPASS splits a clause into two different cases, the two parts will not share variables, i.e. these parts can independently be refuted. For SPASS we implemented powerful reduction rules: tautology deletion, subsumption, condensing, an efficient variant of contextual rewriting,
A Simplifier for Propositional Formulas with Many Binary Clauses
, 2001
"... Deciding whether a propositional formula in conjunctive normal form is satisfiable (SAT) is an NPcomplete problem. The problem becomes linear when the formula contains binary clauses only. Interestingly, the reduction to SAT of a number of wellknown and important problems  such as classical AI p ..."
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Cited by 50 (2 self)
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Deciding whether a propositional formula in conjunctive normal form is satisfiable (SAT) is an NPcomplete problem. The problem becomes linear when the formula contains binary clauses only. Interestingly, the reduction to SAT of a number of wellknown and important problems  such as classical AI planning and automatic test pattern generation for circuits  yields formulas containing many binary clauses. In this paper we introduce and experiment with 2SIMPLIFY, a formula simplifier targeted at such problems. 2SIMPLIFY constructs the transitive closure of the implication graph corresponding to the binary clauses in the formula and uses this graph to deduce new unit literals. The deduced literals are used to simplify the formula and update the graph, and so on, until stabilization. Finally, we use the graph to construct an equivalent, simpler set of binary clauses. Experimental evaluation of this simplifier on a number of benchmark formulas produced by encoding AI planning problems prove 2SIMPLIFY to be a useful tool in many circumstances.