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Computing finite models by reduction to functionfree clause logic
 Journal of Applied Logic
, 2007
"... Recent years have seen considerable interest in procedures for computing finite models of firstorder logic specifications. One of the major paradigms, MACEstyle model building, is based on reducing model search to a sequence of propositional satisfiability problems and applying (efficient) SAT sol ..."
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Cited by 21 (5 self)
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Recent years have seen considerable interest in procedures for computing finite models of firstorder logic specifications. One of the major paradigms, MACEstyle model building, is based on reducing model search to a sequence of propositional satisfiability problems and applying (efficient) SAT solvers to them. A problem with this method is that it does not scale well because the propositional formulas to be considered may become very large. We propose instead to reduce model search to a sequence of satisfiability problems consisting of functionfree firstorder clause sets, and to apply (efficient) theorem provers capable of deciding such problems. The main appeal of this method is that firstorder clause sets grow more slowly than their propositional counterparts, thus allowing for more space efficient reasoning. In this paper we describe our proposed reduction in detail and discuss how it is integrated into the Darwin prover, our implementation of the Model Evolution calculus. The results are general, however, as our approach can be used in principle with any system that decides the satisfiability of functionfree firstorder clause sets. To demonstrate its practical feasibility, we tested our approach on all satisfiable problems from the TPTP library. Our methods can solve a significant subset of these problems, which overlaps but is not included in the subset of problems solvable by stateoftheart finite model builders such as Paradox and Mace4.
Deciding Effectively Propositional Logic using DPLL and substitution sets
"... We introduce a DPLL calculus that is a decision procedure for the BernaysSchönfinkel class, also known as EPR. Our calculus allows combining techniques for efficient propositional search with datastructures, such as Binary Decision Diagrams, that can efficiently and succinctly encode finite sets o ..."
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Cited by 15 (2 self)
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We introduce a DPLL calculus that is a decision procedure for the BernaysSchönfinkel class, also known as EPR. Our calculus allows combining techniques for efficient propositional search with datastructures, such as Binary Decision Diagrams, that can efficiently and succinctly encode finite sets of substitutions and operations on these. In the calculus, clauses comprise of a sequence of literals together with a finite set of substitutions; truth assignments are also represented using substitution sets. The calculus works directly at the level of sets, and admits performing parallel constraint propagation and decisions, resulting in potentially exponential speedups over existing approaches.
Knowledge Representation and Classical Logic
"... Mathematical logicians had developed the art of formalizing declarative knowledge long before the advent of the computer age. But they were interested primarily in formalizing mathematics. Because of the important role of nonmathematical knowledge in AI, their emphasis was too narrow from the perspe ..."
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Cited by 10 (4 self)
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Mathematical logicians had developed the art of formalizing declarative knowledge long before the advent of the computer age. But they were interested primarily in formalizing mathematics. Because of the important role of nonmathematical knowledge in AI, their emphasis was too narrow from the perspective of knowledge representation, their formal languages were not sufficiently expressive. On the other hand, most logicians were not concerned about the possibility of automated reasoning; from the perspective of knowledge representation, they were often too generous in the choice of syntactic constructs. In spite of these differences, classical mathematical logic has exerted significant influence on knowledge representation research, and it is appropriate to begin this handbook with a discussion of the relationship between these fields. The language of classical logic that is most widely used in the theory of knowledge representation is the language of firstorder (predicate) formulas. These are the formulas that John McCarthy proposed to use for representing declarative knowledge in his advice taker paper [176], and Alan Robinson proposed to prove automatically using resolution [236]. Propositional logic is, of course, the most important subset of firstorder logic; recent
Incremental instance generation in local reasoning
 In: Notes 1st CEDAR Workshop, IJCAR 2008
, 2008
"... Abstract. Local reasoning allows to handle SMT problems involving a certain class of universally quantified formulas in a complete way by instantiation to a finite set of ground formulas. We present a method to generate this set incrementally, in order to provide a more efficient way of solving thes ..."
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Cited by 9 (3 self)
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Abstract. Local reasoning allows to handle SMT problems involving a certain class of universally quantified formulas in a complete way by instantiation to a finite set of ground formulas. We present a method to generate this set incrementally, in order to provide a more efficient way of solving these satisfiability problems. The incremental instantiation is guided semantically, inspired by the instance generation approach to firstorder theorem proving. Our method is sound and complete, and terminates on both satisfiable and unsatisfiable input after generating a subset of the instances needed in standard local reasoning. 1
C.: iProvereq – An Instantiationbased Theorem Prover with Equality
 In: IJCAR 2010. LNCS
, 2010
"... Abstract. iProverEq is an implementation of an instantiationbased calculus InstGenEq which is complete for firstorder logic with equality. iProverEq extends the iProver system with superpositionbased equational reasoning and maintains the distinctive features of the InstGen method. In partic ..."
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Cited by 3 (2 self)
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Abstract. iProverEq is an implementation of an instantiationbased calculus InstGenEq which is complete for firstorder logic with equality. iProverEq extends the iProver system with superpositionbased equational reasoning and maintains the distinctive features of the InstGen method. In particular, firstorder reasoning is combined with efficient ground satisfiability checking where the latter is delegated in a modular way to any stateoftheart SMT solver. The firstorder reasoning employs a saturation algorithm making use of redundancy elimination in form of blocking and simplification inferences. We describe the equational reasoning as it is implemented in iProverEq, the main challenges and techniques that are essential for efficiency. 1
An InstantiationBased Theorem Prover for FirstOrder Programming
"... Firstorder programming (FOP) is a new representation language that combines the strengths of mixedinteger linear programming (MILP) and firstorder logic (FOL). In this paper we describe a novel feasibility proving system for FOP formulas that combines MILP solving with instancebased methods from ..."
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Cited by 2 (2 self)
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Firstorder programming (FOP) is a new representation language that combines the strengths of mixedinteger linear programming (MILP) and firstorder logic (FOL). In this paper we describe a novel feasibility proving system for FOP formulas that combines MILP solving with instancebased methods from theorem proving. This prover allows us to perform lifted inference by repeatedly refining a propositional MILP. We prove that this procedure is sound and refutationally complete: if a formula is infeasible our solver will demonstrate this fact in finite time. We conclude by demonstrating an implementation of our decision procedure on a simple firstorder planning problem. 1
System Description: iProver – An InstantiationBased Theorem Prover for FirstOrder Logic
"... Abstract. iProver is an instantiationbased theorem prover which is based on InstGen calculus, complete for firstorder logic. One of the distinctive features of iProver is a modular combination of instantiation and propositional reasoning. In particular, any stateofthe art SAT solver can be inte ..."
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Abstract. iProver is an instantiationbased theorem prover which is based on InstGen calculus, complete for firstorder logic. One of the distinctive features of iProver is a modular combination of instantiation and propositional reasoning. In particular, any stateofthe art SAT solver can be integrated into our framework. iProver incorporates stateoftheart implementation techniques such as indexing, redundancy elimination, semantic selection and saturation algorithms. Redundancy elimination implemented in iProver include: dismatching constraints, blocking nonproper instantiations and propositionalbased simplifications. In addition to instantiation, iProver implements ordered resolution calculus and a combination of instantiation and ordered resolution. In this paper we discuss the design of iProver and related implementation issues. 1
InstGen – A Modular Approach to InstantiationBased Automated Reasoning
"... Abstract. InstGen is an instantiationbased reasoning method for firstorder logic introduced in [18]. One of the distinctive features of InstGen is a modular combination of firstorder reasoning with efficient ground reasoning. Thus, InstGen provides a framework for utilising efficient offthes ..."
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Cited by 1 (1 self)
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Abstract. InstGen is an instantiationbased reasoning method for firstorder logic introduced in [18]. One of the distinctive features of InstGen is a modular combination of firstorder reasoning with efficient ground reasoning. Thus, InstGen provides a framework for utilising efficient offtheshelf propositional SAT and SMT solvers as part of general firstorder reasoning. In this paper we present a unified view on the developments of the InstGen method: (i) completeness proofs; (ii) abstract and concrete criteria for redundancy elimination, including dismatching constraints and global subsumption; (iii) implementation details and evaluation. 1