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SATbased Finite Model Generation for HigherOrder Logic
 PH.D. THESIS, INSTITUT FÃR INFORMATIK, TECHNISCHE UNIVERSITÃT
, 2008
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Proof Translation and SMTLIB Benchmark Certification: A Preliminary Report
 In 6’th International Workshop on SMT
, 2008
"... Satisfiability Modulo Theories (SMT) solvers are large and complicated pieces of code. As a result, ensuring their correctness is challenging. In this paper, we discuss a technique for ensuring soundness by producing and checking proofs. We give details of our implementation using CVC3 and HOL Light ..."
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Satisfiability Modulo Theories (SMT) solvers are large and complicated pieces of code. As a result, ensuring their correctness is challenging. In this paper, we discuss a technique for ensuring soundness by producing and checking proofs. We give details of our implementation using CVC3 and HOL Light and provide initial results from our effort to certify the SMTLIB benchmarks. 1
Ingredients of a Deep Inference Theorem Prover
"... Deep inference deductive systems for classical logic provide exponentially shorter proofs than the sequent calculus systems, however with the cost of higher nondeterminism and larger search space in proof search. We report on our ongoing work on proof search with deep inference deductive systems. We ..."
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Deep inference deductive systems for classical logic provide exponentially shorter proofs than the sequent calculus systems, however with the cost of higher nondeterminism and larger search space in proof search. We report on our ongoing work on proof search with deep inference deductive systems. We present systems for classical logic where nondeterminism in proof search is reduced by constraining the context management rule of these systems. We argue that a deep inference system for classical logic can outperform sequent calculus deductive systems in proof search when nondeterminism and the application of the contraction rule are controlled by means of invertible rules.
Agda as a Platform for the Development of Verified Railway Interlocking Systems
"... This thesis identifies a technological framework that aids the development of verified railway interlocking systems in the Agda theorem prover. The thesis is in two parts, Part I deals with integrating interactive and automated theorem proving in type theory, and Part II addresses verification in th ..."
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This thesis identifies a technological framework that aids the development of verified railway interlocking systems in the Agda theorem prover. The thesis is in two parts, Part I deals with integrating interactive and automated theorem proving in type theory, and Part II addresses verification in the railway domain. Part I presents a selection of techniques that combine automated and interactive theorem proving paradigms. On the automated side, a novel, type theoretic connection between interactive theorem provers and external theorem provers is theoretically developed and implemented for the interactive theorem prover Agda. Also, Part I evaluates the technique against the current stateoftheart techniques for integrating interactive and automated theorem provers. The greatest betterment of the techniques is that it can be feasibly applied to larger industrial problems than existing techniques. When exploring problem sets—mathematical and industrial—we obtained promising results.
Interaction and Depth against Nondeterminism in Proof Search
"... Abstract. Deep inference is a proof theoretical methodology that generalises the traditional notion of inference of the sequent calculus. Deep inference provides more freedom in design of deductive systems for different logics and a rich combinatoric analysis of proofs. In particular, construction o ..."
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Abstract. Deep inference is a proof theoretical methodology that generalises the traditional notion of inference of the sequent calculus. Deep inference provides more freedom in design of deductive systems for different logics and a rich combinatoric analysis of proofs. In particular, construction of exponentially shorter analytic proofs becomes possible, but with the cost of a greater nondeterminism than in the sequent calculus. In this paper, we extend our previous work on proof search with deep inference deductive systems. We argue that, by exploiting an interaction and depth scheme in the logical expressions, the nondeterminism in proof search can be reduced without losing the shorter proofs and without sacrificing from proof theoretical cleanliness. We demonstrate this on deep inference systems for multiplicative linear logic and classical logic. 1