n-tableaux [1] and δ-resolution [2], which are based, respectively, on semantic tableaux and resolution, have been properly used for the resolution of abductive problems. The tool we present is a Prolog implementation of an abductive solver which combines both calculi to attack first order abductive problems by reducing them to finite versions, that is, propositional rewritings of the problems ...

This paper establishes the decidability of SR⊔IQ which has composition-based role Inclusion axioms (RIAs) of the form R1 ◦ · · · ◦ Rn⊑̇T1 ⊔ · · · ⊔ Tm. Also the consistency of an Abox A of SR⊔IQ DL w.r.t. Rbox R is established. Motivation for this kind of RIAs comes from applications in the field of manufactured products as well as other conceptual modeling applications such as family relationsh...

This article uses combinatorial objects called labeled abaci to give direct combinatorial proofs of many familiar facts about Schur polynomials. We use abaci to prove the Pieri rules, the Littlewood–Richardson rule, the equivalence of the tableau definition and the determinant definition of Schur polynomials, and the combinatorial interpretation of the inverse Kostka matrix (first given by Eğec...

Following the approach [Schwind, Risch, 91] to Reiter’s default logic, tiffs paper attempts to define a general tableaux-based framework for tt~c cornlmtation of tile extensions for several known default k)gics. The idea is to qualify the differences b(;twecn the wlriants under considcration inside a single process that can switcil easily from one variant to another. Indeed, the approach is rel...

This paper presents a labelled tableau approach for deciding interrogative-epistemic logics (IEL). Tableau calculi for these logics have been derived using a recently introduced tableau synthesis method. We also consider an extension of the framework for a setting with questioning modalities over sequences of formulae called sequential questioning logic (SQL). We have implemented the calculi us...

In a recent paper, Bentzen proposes a semantically characterised logic called Action Type Deontic Logic, where normative concepts are applied to action expressions, rather than propositional statements. The logic offers solutions to many of the paradoxes of deontic logic. In particular, Bentzen’s semantics solves many puzzles involving the interaction of permission with conjunction and disjunct...

If F is a global function field of characteristic p > 3, we employ Tate’s theory of analytic uniformization to give an alternative proof of a theorem of Igusa describing the image of the natural Galois representation on torsion points of non-isotrivial elliptic curves defined over F . Along the way, using basic properties of Faltings heights of elliptic curves, we offer a detailed proof of the ...

We apply tableau methods to the problem of computing entailment in the nonmonotonic system of equilibrium logic, a generalisation of the inference relation associated with the stable model and answer set semantics for logic programs. We describe tableau calculi for the nonclassical logics underyling equilibrium entailment, namely hereand-there with strong negation and its strengthening classica...

We show that two concepts involving equational provability can be elegantly formalized in terms of a relational algebra, equipped with two special-purpose mappings. We derive some calculus in order to prove that these concepts are equivalent, and that they are sound and complete. We illustrate the use of the relational framework by a few examples. We show how decidability of provability of an e...