A computational logic handbook
A computational logic handbook
Deciding Combinations of Theories
Journal of the ACM (JACM)
Simplification by Cooperating Decision Procedures
ACM Transactions on Programming Languages and Systems (TOPLAS)
Computer-Aided Reasoning: An Approach
Computer-Aided Reasoning: An Approach
A General Setting for Flexibly Combining and Augmenting Decision Procedures
Journal of Automated Reasoning
Incorporating decision procedures in implicit induction
Journal of Symbolic Computation - Integrated reasoning and algebra systems
Constraint contextual rewriting
Journal of Symbolic Computation - Special issue: First order theorem proving
Solving problems by formula manipulation in logic and linear inequalities
IJCAI'71 Proceedings of the 2nd international joint conference on Artificial intelligence
An online proof-producing decision procedure for mixed-integer linear arithmetic
TACAS'03 Proceedings of the 9th international conference on Tools and algorithms for the construction and analysis of systems
Shallow confluence of conditional term rewriting systems
Journal of Symbolic Computation
lim+, δ+, and Non-Permutability of β-Steps
Journal of Symbolic Computation
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To broaden the scope of decision procedures for linear arithmetic, they have to be integrated into theorem provers. Successful approaches e.g. in NQTHM or ACL2 suggest a close integration scheme which augments the decision procedures with lemmas about user-defined operators. We propose an even closer integration providing feedback about the state of the decision procedure in terms of entailed formulas for three reasons: First, to provide detailed proof objects for proof checking and archiving. Second, to analyze and improve the interaction between the decision procedure and the theorem prover. Third, to investigate whether the communication of the state of a failed proof attempt to the human user with the comprehensible standard GUI mechanisms of the theorem prover can enhance the speculation of auxiliary lemmas.