By Maria Paola Bonacina, Moa Johansson (auth.), Kai Brünnler, George Metcalfe (eds.)

This booklet constitutes the refereed court cases of the 20 th foreign convention on automatic Reasoning with Analytic Tableaux and comparable tools, TABLEAUX 2011, held in Bern, Switzerland, in July 2011.The sixteen revised learn papers provided including 2 process descriptions have been conscientiously reviewed and chosen from 34 submissions. The papers conceal many issues within the wide selection of functions of tableaux and similar tools equivalent to analytic tableaux for numerous logics, comparable options and ideas, comparable equipment, new calculi and techniques for theorem proving in classical and non-classical logics, in addition to structures, instruments, implementations and purposes; all with a unique specialize in and software program verifications, semantic applied sciences, and data engineering.

**Read Online or Download Automated Reasoning with Analytic Tableaux and Related Methods: 20th International Conference, TABLEAUX 2011, Bern, Switzerland, July 4-8, 2011. Proceedings PDF**

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**Additional info for Automated Reasoning with Analytic Tableaux and Related Methods: 20th International Conference, TABLEAUX 2011, Bern, Switzerland, July 4-8, 2011. Proceedings**

**Sample text**

Replacing the previous conjunction by its image by Δ yields a schema that is actually identical to the ﬁrst one. Hence the procedure stops (no further schema is generated) and we get Eρ∗ ◦unfold (φ) = {φ}. By Theorem 2, the T -satisﬁability of φ is thus equivalent to the one of φ{n ← 0} which can be easily tested by any SMT-solver. Example 6. Consider the algorithm below, counting the number of occurrences o of an element e in an array t. We want to check that if the ﬁnal value of o is 1 then the formula ∀i, j, ai ≈ e ∧ aj ≈ e ⇒ i ≈ j holds.

If u and v occur in θ(a), then the considered schema will possibly contain a conjunction of the form an+2 ≈ u∧an+2 ≈ v. 2, the symbol an+2 will have to be eliminated (since it is non-n-elementary) by applying an appropriate function Δ. But to this purpose, one necessarily has to ensure that the equation u ≈ v holds. The existence of the function τ guarantees that this property can be expressed as an n-elementary schema. 3. Schemata of SMT-Problems 39 Definition 9. Let L be the set of literals λ satisfying one of the following conditions: - λ is of the form u v 5 , where each of the u, v is either a non-indexed term or of the form aα where a ∈ C and α ∈ {n, n + 1, n + 2, i, i + 1}.

A ∧ a ≈ a ∧ · · · ∧ a i i i i ≈ ai+1 i+1 i=0 - Additional parameters. Inequalities of the form i ≤ m where m is an additional parameter interpreted as an element of [0, n] can be encoded by atoms n ≤m ≤m ≤m ≤m p≤m i deﬁned by the following axioms: ¬pn+1 ∧ p0 ∧ i=0 (pi+1 ⇒ pi ). Then n ≤m ≤m i ≈ m can be deﬁned using i=0 (p=m i ⇔ pi ∧ ¬pi+1 ) and a disequality m ≈ k n =k can be tested by the schema: i=0 (¬p=m i ∨ ¬pi ). - Using the parameter in iteration bodies. A term of the form an can be replaced by a fresh non-indexed constant b, with the axiom: b ≈ an .