The first step towards a wide-coverage tableau prover for natural logic is presented. We describe an automatized method for obtaining Lambda Logical Forms from surface forms and use this method with an implemented prover to hunt for new tableau rules in textual entailment data sets. The collected tableau rules are presented and their usage is also exemplified in several tableau proofs. The perf...

With the help of a tableaux method, determinant formulas for trace generating functions for various classes of shifted plane partitions are derived. Proceeding from these determinants, generalizations of Gansner's (J. hook formulas for shifted plane partitions and alternative proofs of recent results of Proctor about alternating trace generating functions are given.

An overview is provided of some of the basic facts concerning rim hook lattices and ribbon tableaux, using a representation of partitions by their edge sequences. An action is defined of the affine Coxeter group of type Ãr−1 on the r-rim hook lattice, and thereby on the sets of standard and semistandard r-ribbon tableaux, and this action is related to the concept of chains in r-ribbon tableaux....

We characterise those classes of permutations closed under taking subsequences and reindexing that also have the property that for every tableau shape either every permutation of that shape or no permutation of that shape belongs to the class. The characterisation is in terms of the dominance order for partitions (and their conjugates) and shows that for any such class there is a constant k suc...

We describe a general and uniform tableau methodology for multi-modal logics arising from Gabbay’s methodology of fibring and Governatori’s tableau system KEM.

In this paper, diierent variants of classical analytic calculi for rst-order logic are compared with respect to the length of proofs possible in such calculi. A cut-free sequent calculus is used as a prototype for diierent other analytic calculi like analytic tableau or various connection calculi. With modiied branching rules ({rules), non-elementary shorter minimal proofs can be obtained for a...

To decide whether two permutations are comparable in Bruhat order of Sn with the well-known tableau criterion requires ( n 2 ) comparisons of entries in certain sorted arrays. We show that to decide whether x ≤ y only d1 + d2 + . . .+ dk of these comparisons are needed, where {d1, d2, . . . , dk} = {i|x(i) > x(i+1)}. This is obtained as a consequence of a sharper version of Deodhar’s criterion,...

The current generation of rewriting-algorithms in source-centric (local-as-view) information integration systems all produce a reformulated query that retrieves what has been thought of as ”the best obtainable” answer, given the circumstances that the source-centric approach introduces incomplete information into the virtual global relations. This ”best obtainable” answer does not however allow...

The possible worlds model and its associated Kripkean semantics provide an intuitive semantics to epistemic logics, but they seem to commit us to model agents which are logically omniscient and perfect reasoners. In this article we show that this is not necessarily the case, if possible worlds are not considered as consistent descriptions of the real world. We propose to model the beliefs of an...

In resolution proof procedures refinements based on A-orderings of literals have a long tradition and are well investigated. In tableau proof proceduressuch refinements were only recently introduced by the authors of the present paper. In this paper we prove the following results: we give a completeness proof of A-ordered ground clause tableaux which is a lot easier to follow than the previous ...