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Ordered Semantic HyperLinking
, 1994
"... We propose a method for combining the clause linking theorem proving method with theorem proving methods based on orderings. This may be useful for incorporating termrewriting based approaches into clause linking. In this way, some of the propositional inefficiencies of orderingbased approaches ..."
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Cited by 24 (3 self)
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We propose a method for combining the clause linking theorem proving method with theorem proving methods based on orderings. This may be useful for incorporating termrewriting based approaches into clause linking. In this way, some of the propositional inefficiencies of orderingbased approaches may be overcome, while at the same time incorporating the advantages of ordering methods into clause linking. The combination also provides a natural way to combine resolution on nonground clauses, with the clause linking method, which is essentially a ground method. We describe the method, prove completeness, and show that the enumeration part of clause linking with semantics can be reduced to polynomial time in certain cases. We analyze the complexity of the proposed method, and also give some plausibility arguments concerning its expected performance. 1 Introduction There are at least two basic approaches to the study of automated deduction. One approach concentrates on solving...
Proof Lengths for Equational Completion
 Information and Computation
, 1995
"... We first show that ground termrewriting systems can be completed in a polynomial number of rewriting steps, if the appropriate data structure for terms is used. We then apply this result to study the lengths of critical pair proofs in nonground systems, and obtain bounds on the lengths of critical ..."
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Cited by 15 (1 self)
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We first show that ground termrewriting systems can be completed in a polynomial number of rewriting steps, if the appropriate data structure for terms is used. We then apply this result to study the lengths of critical pair proofs in nonground systems, and obtain bounds on the lengths of critical pair proofs in the nonground case. We show how these bounds depend on the types of inference steps that are allowed in the proofs. 1 Introduction We are interested in developing theoretical techniques for evaluating the efficiency of automated inference methods. This includes bounding proof sizes, as well as bounding the size of the total search space generated. Such investigations can provide insights into the comparative strengths of various inference systems, insights that might otherwise be missed. This can also aid in the development of new methods and new inference rules, as we will show. We first consider equational deduction for systems of ground equations. We note that in general...
Proving with BDDs and Control of Information
 In: CADE12
, 1995
"... . We present a new automated proof method for firstorder classical logic, aimed at limiting the combinatorial explosion of the search. It is nonclausal, based on BDDs (binary decision diagrams) and on new strategies that control the size and traversal of the search space by controlling the amount ..."
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Cited by 5 (1 self)
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. We present a new automated proof method for firstorder classical logic, aimed at limiting the combinatorial explosion of the search. It is nonclausal, based on BDDs (binary decision diagrams) and on new strategies that control the size and traversal of the search space by controlling the amount of information, in Shannon's sense, gained at each step of the proof. Our prover does not search blindly for a proof, but thinks a lot to decide of a course of action. Practical results show that this pays off. 1 Introduction We present a complete refutation method for firstorder classical logic that aims at controlling the growth and at guiding the traversal of the search space intelligently. Our starting point is [10], which proves that finding whether a given proposition in this logic is obvious, for several different reasonable definitions of nonobviousness, is \Sigma p 2 complete. This not only means that proving is hard, but also that any complete proof method is built on, or hid...
MachineIndependent Evaluation of TheoremProving Strategies
, 1997
"... ic programming and all applications of deduction. The idea of "strategy analysis" is new. Most of the work on search in artificial intelligence concentrates on the design of heuristics (e.g., [5]). Most of the research in complexity related to theorem proving studies the complexity of propositional ..."
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Cited by 1 (1 self)
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ic programming and all applications of deduction. The idea of "strategy analysis" is new. Most of the work on search in artificial intelligence concentrates on the design of heuristics (e.g., [5]). Most of the research in complexity related to theorem proving studies the complexity of propositional proofs as part of the quest for NP 6= co\GammaN P (e.g., see [10] for a survey), or works with complexity measures based on the Herbrand theorem to determine lower bounds for sets of clauses, not upper bounds for strategies (e.g., [2, 4, 7]). In resolution theorem proving, the classical source for the modelling of search is [3], which was not concerned with evaluating the complexity of the strategies. The primary objective of strategy analysis is to study the complexity of searching for a proof. An approach to this problem was proposed in [6]. It applies classical techniques from algorithm analysis to derive worstcase upper
Efficient FirstOrder Semantic Deduction Techniques
, 1998
"... Mathematical logic formalizes the process of mathematical reasoning. For centuries, it has been a dream of mathematicians to do mathematical reasoning mechanically. In the TPTP library, one finds thousands of problems from various domains of mathematics such as group theory, number theory, set theor ..."
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Cited by 1 (0 self)
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Mathematical logic formalizes the process of mathematical reasoning. For centuries, it has been a dream of mathematicians to do mathematical reasoning mechanically. In the TPTP library, one finds thousands of problems from various domains of mathematics such as group theory, number theory, set theory, etc. Many of these problems can now be solved with state of the art automated theorem provers. Theorem proving also has applications in artificial intelligence and formal verification. As a formal method, theorem proving has been used to verify the correctness of various hardware and software designs. In this thesis, we propose a novel firstorder theorem proving strategy  ordered semantic hyper linking (OSHL). OSHL is an instancebased theorem proving strategy. It proves firstorder unsatisfiability by generating instances of firstorder clauses and proving the set of instances to be propositionally unsatisfiable. OSHL can use semantics, i.e. domain information, to guide its search. OS...
Encoding First Order Proofs in SAT
"... Abstract. We present a method for proving rigid first order theorems by encoding them as propositional satisfiability problems. We encode the existence of a first order tableau and the satisfiability of unification constraints. Then the first order theorem is rigidly unsatisfiable if and only if the ..."
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Abstract. We present a method for proving rigid first order theorems by encoding them as propositional satisfiability problems. We encode the existence of a first order tableau and the satisfiability of unification constraints. Then the first order theorem is rigidly unsatisfiable if and only if the encoding is propositionally satisfiable. We have implemented this method in our theorem prover CHEWTPTP, and present experimental results. This method can be useful for general first order problems, by continually adding more instances of each clause. Rigid theorem proving itself is also directly applicable to problems of cryptographic protocol analysis. 1
Encoding First Order Proofs in SMT
, 2007
"... We present a method for encoding first order proofs in SMT. Our implementation, called ChewTPTPSMT, transforms a set of first order clauses into a propositional encoding (modulo theories) of the existence of a rigid first order connection tableau and the satisfiability of unification constraints, w ..."
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We present a method for encoding first order proofs in SMT. Our implementation, called ChewTPTPSMT, transforms a set of first order clauses into a propositional encoding (modulo theories) of the existence of a rigid first order connection tableau and the satisfiability of unification constraints, which is then fed to Yices. For the unification constraints, terms are represented as recursive datatypes, and unification constraints are equations on terms. The finiteness of the tableau is encoded by linear real arithmetic inequalities. We compare our implementation with our previous implementation ChewTPTPSAT, encoding rigid connection tableau in SAT, and show that for Horn clauses many fewer propositional clauses are generated by ChewTPTPSMT, and ChewTPTPSMT is much faster than ChewTPTPSAT. This is not the case for our nonHorn clause encoding. We explain this, and we conjecture a rule of thumb on when to use theories in encoding a problem. 1