This paper presents the first systematic treatment of tableau calculi for modal logic K with global counting operators. Using a recently introduced tableau synthesis framework we establish two terminating tableau calculi for the logic. Whereas the first calculus is a prefix tableau calculus, the second is a refinement that internalises the semantics of the logic without using nominals. We prove...

The paper is devoted to an approach to analytic tableaux for propositional logic, but can be successfully extended to other logics. The distinguishing features of the presented approach are: (i) a precise set-theoretical description of tableau method; (ii) a notion of tableau consequence relation is defined without help of a notion of tableau, in our universe of discourse the basic notion is a ...

A tableau inversion is a pair of entries in row-standard tableau T that lie in the same column of T yet lack the appropriate relative ordering to make T columnstandard. An i-inverted Young tableau is a row-standard tableau along with precisely i inversion pairs. Tableau inversions were originally introduced by Fresse to calculate the Betti numbers of Springer fibers in Type A, with the number o...

It has been shown that the sequence of Smith invariants defined by certain sequences of products of matrices, with entries in a local principal ideal domain, are combinatorially described by tableau-pairs (T, K) where T is a tableau of skew-shape which rectifies to the key-tableau K. It is a fact that the set of all shuffles of the columns of a key-tableau is a subset of its Knuth class. Here, ...

We give degree formulas for Grothendieck polynomials indexed by vexillary permutations and 1432-avoiding via tableau combinatorics. These generalize a formula degrees of symmetric which appeared in previous joint work the authors with Y. Ren A. St. Dizier. apply our to compute Castelnuovo-Mumford regularity classes generalized determinantal ideals. In particular, we combinatorial regularities a...

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 this paper, we focus our attention on tableau methods for propositional interval temporal logics. These logics provide a natural framework for representing and reasoning about temporal properties in several areas of computer science. However, while various tableau methods have been developed for linear and branching time point-based temporal logics, not much work has been done on tableau met...

This paper investigates the relationship between automataand tableau-based inference procedures for Description Logics. To be more precise, we develop an abstract notion of what a tableau-based algorithm is, and then show, on this abstract level, how tableau-based algorithms can be converted into automata-based algorithms. In particular, this allows us to characterize a large class of tableau-b...