There are various cases in physics and engineering sciences (specially communications) where one requires the envelope PDF of the sum of several random sinusoidal signals. According to the correspondence between a random sinusoidal signal and a random vector, sum of random vectors can be considered as an abstract mathematical model for the above sum. Now it is desired to obtain the PDF of the l...

We introduce a generic framework for hybrid logics, i.e. modal logics additionally featuring nominals and satisfaction operators, thus providing the necessary facilities for reasoning about individual states in a model. This framework, coalgebraic hybrid logic, works at the same level of generality as coalgebraic modal logic, and in particular subsumes, besides normal hybrid logics such as hybr...

Axiom pinpointing has been introduced in description logics (DLs) to help the user to understand the reasons why consequences hold and to remove unwanted consequences by computing minimal (maximal) subsets of the knowledge base that have (do not have) the consequence in question. The pinpointing algorithms described in the DL literature are obtained as extensions of the standard tableau-based r...

Walks on Young’s lattice of integer partitions encode many objects of algebraic and combinatorial interest. Chen et al. established connections between such walks and arc diagrams. We show that walks that start at ∅, end at a row shape, and only visit partitions of bounded height are in bijection with a new type of arc diagram – open diagrams. Remarkably two subclasses of open diagrams are equi...

The aim of this work is to provide a general method to minimize the size (number of states) of a model M of an ATL∗ formula. Our approach is founded on the notion of alternating bisimulation: given a model M, it is transformed in a stepwise manner into a new model M’ minimal with respect to bisimulation. The method has been implemented and will be integrated to the prover TATL, that constructiv...

b b b b b b b b b b b b b b b b b b b Abstract Proof procedures based on model elimination or the connection tableau calculus have become more and more successful in the past. But these procedures still suuer from long proof lengths as well as from a rather high degree of redundant search eeort in comparison to resolution-style search procedures. In order to overcome these problems we investiga...

The verification process of reactive systems in local model checking [2, 9, 28] and in explicit state model checking [14, 16] is on-the-fly. Therefore only those states of a system have to be traversed that are necessary to prove a property. In addition, if the property does not hold, than often only a small subset of the state space has to be traversed to produce a counterexample. Global model...

We present a tableau-based construction for obtaining an automaton from a temporal logic formula in an “on-the-fly” fashion. That is, the automaton can be constructed simultaneously with, and guided by, the generation of the model. In particular, it is possible to detect that a property does not hold by only constructing part of the model and of the automaton. The algorithm can also be used to ...

Let us recall that Raphael Robinson’s Arithmetic Q is an axiom system that differs from Peano Arithmetic essentially by containing no Induction axioms [13, 18]. We will generalize the semantictableaux version of the Second Incompleteness Theorem almost to the level of System Q. We will prove that there exists a single rather long Π1 sentence, valid in the standard model of the Natural Numbers a...

The goal of this paper is to propose a new technique for developing decision procedures for propositional modal logics. The basic idea is that propositional modal decision procedures should be developed on top of propositional decision procedures. As a case study, we describe an algorithm, based on an implementation of the Davis-Putnam-Longemann-Loveland procedure, which tests satissability in ...