By Gilles Dowek (auth.), Robert Nieuwenhuis (eds.)
This ebook constitutes the refereed lawsuits of the twentieth foreign convention on computerized Deduction, CADE-20, held in Tallinn, Estonia, in July 2005.
The 25 revised complete papers and five method descriptions awarded have been conscientiously reviewed and chosen from seventy eight submissions. All present facets of computerized deduction are addressed, starting from theoretical and methodological matters to presentation and review of theorem provers and logical reasoning platforms.
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Extra info for Automated Deduction – CADE-20: 20th International Conference on Automated Deduction, Tallinn, Estonia, July 22-27, 2005. Proceedings
Xα M] ∈ prop(S). We use the notation . , ∨ . and ∀. to distinguish these constructors (at the level of propositions) from the corresponding logical constants , ¬, ∨ and Π α . Suppose S is a signature with ¬ ∈ S and A ∈ wﬀo (S). Then ¬A ∈ wﬀo (S) is both a term of type o and a proposition. Also, A is a term of type o and a proposition. Hence ¬ . A is a proposition, but is not a term of type o. We assume the usual notions of α, β and η conversion for terms. These can be easily extended (by induction) to propositions along with notions of substitution, β-normalization, βη-normalization, etc.
Poo ⊥o ] ∨ . [P [¬ ]]. An expansion tree for this formula is shown on the left in Figure 2. We could try to connect LEAF0 to LEAF1, but we will never be able to syntactically unify [P ⊥] and [P [¬ ]]. Extensionally, we can prove these are equal since the arguments ⊥ and ¬ are equivalent, hence equal by Boolean extensionality. n extensional expansion dag which would provide a proof of the sentence is shown on the right in Figure 2. We make the connection between ATOM0 and ATOM1 explicit via the connection node MATE.
Design a set of search operations for approximating compact ground proofs (using variables). 4. Establish completeness of search by verifying that some selection of the search operations will lead to a proof, if a proof exists. R. ): CADE 2005, LNAI 3632, pp. 23–37, 2005. E. Brown A ground expansion proof can be approximated by an expansion tree with expansion variables. First-order methods can be naturally generalized to search for expansion proofs. In particular, Tps combines mating search with Huet’s higher-order pre-uniﬁcation.
Automated Deduction – CADE-20: 20th International Conference on Automated Deduction, Tallinn, Estonia, July 22-27, 2005. Proceedings by Gilles Dowek (auth.), Robert Nieuwenhuis (eds.)