The spectrum of a first-order logic sentence is the set of natural numbers that are cardinalities of its finite models. In this paper we show that when restricted to using only two variables, but allowing counting quantifiers, the class of spectra of first-order logic sentences is exactly the class of semilinear sets and, hence, closed under complement. At the heart of our proof are semilinear ...

In this paper, we propose an EXPSPACE tableau-based algorithm for SHOIQ. The construction of this algorithm is founded on the standard tableaubased method for SHOIQ and the technique used for designing a NEXPTIME algorithm for the two-variable fragment of first-order logic with counting quantifiers C.

The finite satisfiability problem for the two-variable fragment of first-order logic interpreted over trees was recently shown to be ExpSpace-complete. We consider two extensions of this logic. We show that adding either additional binary symbols or counting quantifiers to the logic does not affect the complexity of the finite satisfiability problem. However, combining the two extensions and ad...

The satisfiability and finite satisfiability problems for the two-variable fragment of first-order logic with counting were shown in [5] to be in NExpTime. This paper presents a simplified proof via a result on integer programming due to Eisenbrand and Shmonina [2].

This study summarizes results from a preliminary evaluation of the Hybrid III Large Male Dummy. The paper reviews the dimensions, certification test responses, durability, and repeatability and reproducibility of two Hybrid III 95 Percentile Large Male dummies, each produced by a different manufacturer. Response data from multiple repeats of the proposed Calibration and Inspection Test Procedur...

Interval-based temporal logics are an important research area in computer science and artificial intelligence. In this paper we investigate decidability and expressiveness issues for Propositional Neighborhood Logics (PNLs). We begin by comparing the expressiveness of the different PNLs. Then, we focus on the most expressive one, namely, PNL, and we show that it is decidable over various classe...

Data trees and data words have been studied extensively in connection with XML reasoning. These are trees or words that, in addition to labels from a finite alphabet, carry labels from an infinite alphabet (data). While in general logics such as MSO or FO are undecidable for such extensions, decidablity results for their fragments have been obtained recently, most notably for the two-variable f...

We consider a modified version of the situation calculus built using a two-variable fragment of the first-order logic extended with counting quantifiers. We mention several additional groups of axioms that need to be introduced to capture taxonomic reasoning. We show that the regression operator in this framework can be defined similarly to regression in the Reiter’s version of the situation ca...