Resolution reasoners, when applied to set theory problems, typically suffer from “lack of focus.” MARS is a program that attempts to rectify this difficulty by exploiting the definition-like character of the set theory axioms. As in the case of its predecessor, SLIM, it employs a tableau proof procedure based on binary resolution, but MARS IS enhanced by an equality substitution rule and a devi...

We summarize and reorganize some of the last decade's research on real-time extensions of temporal logic. Our main focus is on tableau constructions for model checking linear temporal formulas with timing constraints. In particular, we nd that a great deal of real-time veri cation can be performed in polynomial space, but also that considerable care must be exercised in order to keep the real-t...

Although description logic systems can adequately be used for representing and reasoning about underspecified information (e.g., for John we know he is French or Italian), in practical applications it can be assumed that (only) for some tasks the expressivity of description logics really comes into play whereas for building complete applications, it is often necessary to effectively solve insta...

This is an examination of similarities and differences between two recent models of abductive reasoning. The one is developed in Atocha Aliseda’s Abductive Reasoning: Logical Investigations into the Processes of Discovery and Evaluation (2006). The other is advanced by Dov Gabbay and the present author in their The Reach of Abduction: Insight and Trial (2005). A principal difference between the...

Our recent work in [1] exhibits a canonical basis of the Garsia-Procesi module Rλ with cells labeled by standard tableaux of catabolizability D λ. Through our study of the Kazhdan-Lusztig preorder on this basis, we found a way to transform a standard word labeling a basis element into a word inserting to the unique tableau of shape λ. This led to an algorithm that computes the catabolizability ...

We extend the unquantiied set-theoretic fragment discussed in 1] with a restricted form of quantiication, we prove decidability of the resulting fragment by means of a tableau calculus and we address the eeciency problem of the underlying decision procedure, by showing that the model-checking steps used in 1] are not necessary.

Axiom-Pinpointing bestimmt die für eine Konsequenz verantwortlichen Axiome einer Ontologie und unterstützt dadurch die Suche und Behebung von Fehlern. In der Arbeit [Peñ09b], deren Resultate hier zusammengefasst werden, wurde untersucht, unter welchen Bedingungen sich tableau-artige und auf automaten-basierte Schlußfolgerungsverfahren für Beschreibungslogiken stets zu Pinpointing-Verfahren erwe...

In this paper we focus our attention on the decision problem for Propositional Neighborhood Logic (PNL for short). PNL is the proper subset of Halpern and Shoham’s modal logic of intervals whose modalities correspond to Allen’s relations meets and met by. We show that the satisfiability problem for PNL over the integers is NEXPTIME-complete. Then, we develop a sound and complete tableau-based d...

We define mosaics, which are naturally in bijection with Knutson-Tao puzzles. We define an operation on mosaics, which shows they are also in bijection with Littlewood-Richardson skew-tableaux. Another consequence of this construction is that we obtain bijective proofs of commutativity and associativity for the ring structures defined either of these objects. In particular, we obtain a new, eas...

The speci cation of communication behavior is fundamental in devel oping interoperable transactions In particular the temporal ordering of messages exchanged between di erent communicating agents must be declar atively speci ed and veri ed in order to guarantee consistency of data in the various component systems This paper shows that by expressing communi cation constraints in propositional te...