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Proof Search without Backtracking using Instance Streams
 In Proc. Int. Workshop on FirstOrder Theorem Proving
, 2000
"... ms are a way of organizing the search for instances which close a proof. The basic idea is as follows: To close a proof with two branches, one needs to nd an instantiation for the free variables, that allows to close both of them. So one rst expands the rst branch, until a closing instance is found. ..."
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ms are a way of organizing the search for instances which close a proof. The basic idea is as follows: To close a proof with two branches, one needs to nd an instantiation for the free variables, that allows to close both of them. So one rst expands the rst branch, until a closing instance is found. Then, one does the same for the second branch. If these two instances are compatible, they may be joined to give an instance that closes both branches simultaneously. Otherwise, the rst two instances are remembered, and further instances closing each of the two branches are sought, by expanding them if necessary. Each instance that closes one branch is checked for compatibility with all of the instances that have been found for the other one. As soon as two of these instances are compatible, the joint instance closes both branches simultaneously. This process is applied recursively, if one of the two branches splits further. No backtracking, and no iterative deepening ar
Model Building for Natural Language Understanding
 in: Proceedings of ICoS4
, 2001
"... Contents 1 Introduction 1 2 Model Building 3 2.1 FirstOrder Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 2.2 Constructing Models for Logical Theories . . . . . . . . . . . . . . . . . . . . . . . 4 2.3 Inconsistent Theories . . . . . . . . . . . . . . . . . . . . ..."
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Contents 1 Introduction 1 2 Model Building 3 2.1 FirstOrder Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 2.2 Constructing Models for Logical Theories . . . . . . . . . . . . . . . . . . . . . . . 4 2.3 Inconsistent Theories . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 3 Linguistic Applications 5 3.1 Information Seeking Dialogue . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 3.2 Controlling a Mobile Robot . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 3.3 Question Answering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 4 Using Inference Tools 8 4.1 Automated Model Builders . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 4.2 Automated Theorem Provers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 4.3 System Integration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10<F18.67
Duality for GoalDriven Query Processing in Disjunctive Deductive Databases
 Journal of Automated Reasoning
, 2002
"... Bottomup query answering procedures tend to explore a much larger search space than what is strictly needed. Topdown processing methods use the query to perform a more focused search which can result in more efficient query answering. Given a Disjunctive Deductive Database, DB, and a query Q, w ..."
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Bottomup query answering procedures tend to explore a much larger search space than what is strictly needed. Topdown processing methods use the query to perform a more focused search which can result in more efficient query answering. Given a Disjunctive Deductive Database, DB, and a query Q, we establish a strong connection between model generation and clause derivability in two different representations of DB and Q. This allows us to use a bottomup procedure for evaluating Q against DB in a topdown fashion. The approach requires no extensive rewriting of the input theory and introduces no new predicates. Rather, it is based on a certain duality principle for interpreting logical connectives. The duality transformation is achieved by reversing the direction of implication arrows in the clauses representing both the theory and the negation of the query. The application of a generic bottomup procedure to the transformed clause set results in topdown query answering. Under favorable conditions efficiency gains are substantial as shown by our preliminary testing. We give the logical meaning of the duality transformation and point to the conditions and sources of improved efficiency.
Generalizing DPLL and satisfiability for equalities
 Journal of Information and Computation
, 2004
"... Abstract. We present GDPLL, a generalization of the DPLL procedure. It solves the satisfiability problem for decidable fragments of quantifierfree firstorder logic. Sufficient conditions are identified for proving soundness, termination and completeness of GDPLL. We show how the original DPLL proce ..."
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Abstract. We present GDPLL, a generalization of the DPLL procedure. It solves the satisfiability problem for decidable fragments of quantifierfree firstorder logic. Sufficient conditions are identified for proving soundness, termination and completeness of GDPLL. We show how the original DPLL procedure is an instance. Subsequently the GDPLL instances for equality logic, and the logic of equality over infinite ground term algebras are presented. Based on this, we implemented a decision procedure for inductive datatypes. We provide some new benchmarks, in order to compare variants.
Solving satisfiability in ground logic with equality by efficient conversion to propositional logic
 In Proceedings of the 7th Symposium on Abstraction, Reformulation, and Approximation
, 2007
"... Abstract Ground Logic with Equality (GL = ) is a subset of FirstOrder Logic (FOL) in which functions or quantifiers are excluded, but equality is preserved. We argue about GL = ’s unique position (in terms of expressiveness and ease of decidability) between FOL and Propositional Logic (PL). We aim ..."
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Abstract Ground Logic with Equality (GL = ) is a subset of FirstOrder Logic (FOL) in which functions or quantifiers are excluded, but equality is preserved. We argue about GL = ’s unique position (in terms of expressiveness and ease of decidability) between FOL and Propositional Logic (PL). We aim to solve satisfiability (SAT) problems formulated in GL = by converting them into PL using a satisfiabilitypreserving conversion algorithms, and running a general SAT solver on the resulting PL Knowledge Base (KB). We introduce two conversion algorithms, with the latter utilizing the former as a subroutine, and prove their correctness that is, that the translation preserves satisfiability. The main contribution of this work is in utilizing input fragmentation to yield PL KBs that are smaller than possible prior to our work, thus resulting in the ability to solve GL = SAT problems faster than was possible before. 1
Firstorder resolution methods for modal logics
 In Volume in Memoriam of Harald Ganzinger, LNCS
, 2006
"... Abstract. In this paper we give an overview of results for modal logic which can be shown using techniques and methods from firstorder logic and resolution. Because of the breadth of the area and the many applications we focus on the use of firstorder resolution methods for modal logics. In additi ..."
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Abstract. In this paper we give an overview of results for modal logic which can be shown using techniques and methods from firstorder logic and resolution. Because of the breadth of the area and the many applications we focus on the use of firstorder resolution methods for modal logics. In addition to traditional propositional modal logics we consider more expressive PDLlike dynamic modal logics which are closely related to description logics. Without going into too much detail, we survey different ways of translating modal logics into firstorder logic, we explore different ways of using firstorder resolution theorem provers, and we discuss a variety of results which have been obtained in the setting of firstorder resolution. 1
Three Stories on Automated Reasoning for Natural Language Understanding
 in: Proceedings of ESCoR (IJCAR Workshop): Empirically Successful Computerized Reasoning
, 2006
"... Three recent applications of computerised reasoning in natural language processing are presented. The first is a text understanding system developed in the late 1990s, the second is a spokendialogue interface to a mobile robot and automated home, and the third is a system that determines textual en ..."
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Three recent applications of computerised reasoning in natural language processing are presented. The first is a text understanding system developed in the late 1990s, the second is a spokendialogue interface to a mobile robot and automated home, and the third is a system that determines textual entailment. In all of these applications, offtheshelf tools for reasoning with firstorder logic (theorem provers as well as model builders) are employed to assist in natural language understanding. This overview is not only an attempt to identify the added value of computerised reasoning in natural language understanding, but also to point out the limitations of the firstorder inference techniques currently used in natural language processing.
Automated Reasoning: Past Story and New Trends*
"... We overview the development of firstorder automated reasoning systems starting from their early years. Based on the analysis of current and potential applications of such systems, we also try to predict new trends in firstorder automated reasoning. Our presentation will be centered around two main ..."
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We overview the development of firstorder automated reasoning systems starting from their early years. Based on the analysis of current and potential applications of such systems, we also try to predict new trends in firstorder automated reasoning. Our presentation will be centered around two main motives: efficiency and usefulness for existing and future potential applications. This paper expresses the views of the author on past, present, and future of theorem proving in firstorder logic gained during ten years of working on the development, implementation, and applications of the theorem prover Vampire, see [Riazanov and Voronkov, 2002a]. It reflects our recent experience with applications of Vampire in verification, proof assistants, theorem proving, and semantic Web, as well as the analysis of future potential applications. 1 Theorem Proving in FirstOrder Logic The idea of automatic theorem proving has a long history both in mathematics and computer science. For a long time, it was believed by many that hard theorems in mathematics can be proved in a completely automatic way, using the ability of computers to perform fast combinatorial calculations. The very first experiments in automated theorem proving have shown that the purely combinatorial methods of proving firstorder theorems are too week even for proving theorems regarded as relatively easy by mathematicians. Provability in firstorder logic is a very hard combinatorial problem. Firstorder logic is undecidable, which means that there is no terminating procedure checking provability of formulas. There are decidable classes of firstorder formulas but formulas of these classes do not often arise in applications. Due to undecidability, very short formulas may turn out to be extremely complex, while very long ones rather easy. Sometimes firstorder provers find proofs consisting of several thousand steps in a few seconds, but sometimes it takes hours to find a tenstep proof. The theory of firstorder reasoning is centered around the completeness theorems while in practice completeness is often not an issue due to the intrinsic * Partially supported by a grant from EPSRC.
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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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