The automatic verification of computer programs is an important step in software engineering. In this regard temporal logics have been invented as an extension of modal logic which itself is an extension of propositional logic. Therefore, one may call them modal logic variants. The first part of this thesis will investigate the two temporal logics CTL and CTL? with respect to their model checki...

Alchourrón devoted his last years to the analysis of the notion of defeasible conditionalization. He developed a formal system capturing the essentials of this notion. His definition of the defeasible conditional is given in terms of strict implication operator and a modal operator f which is interpreted as a revision function at the language level. In this paper, we will point out that this un...

Abstract In this paper, we apply relating semantics to the widely discussed problem of free choice between permitted actions or situations in normative systems. Leaving aside contexts which principle is obviously unacceptable (weak permission understood as an absence prohibition) uncontroversially valid (strong within systems with a closed repertoire situations), concentrate on for explicit per...

For a finite-dimensional operator A with spectrum σ(A), the following conditions on the Davis–Wielandt shell DW (A) of A are equivalent: (a) A is normal. (b) DW (A) is the convex hull of the set {(λ, |λ|) : λ ∈ σ(A)}. (c) DW (A) is a polyhedron. These conditions are no longer equivalent for an infinite-dimensional operator A. In this note, a thorough analysis is given for the implication relati...

We consider the problem of recovering the coefficient q(x) in the equation ut = ∆u− qu from boundary observations. Uniqueness of q based on knowledge of the ‘Neumann 7→Dirichlet response operator’ is shown as an implication of (known) corresponding results concerning the inverse problem for the corresponding hyperbolic equation wtt = ∆w − qw. This is then reduced to use of the response to a sin...

We consider trigonometric solutions of WDVV equations and derive geometric conditions when a collection of vectors with multiplicities determines such a solution. We incorporate these conditions into the notion of trigonometric Veselov system (∨-system) and we determine all trigonometric ∨-systems with up to five vectors. We show that generalized Calogero-Moser-Sutherland operator admits a fact...

Recent studies have shown that with appropriate operator decision support and with sufficient automation, inverting the multiple operators to single-unmanned vehicle control paradigm is possible. These studies, however, have generally focused on homogeneous teams of vehicles, and have not completely addressed either the manifestation of heterogeneity in vehicle teams, or the effects of heteroge...

We consider the problem of recovering the coeecient q(x) in the equation u t = u ? qu from boundary observations. Uniqueness of q based on knowledge of thèNeumann 7 !Dirichlet response operator' is shown as an implication of (known) corresponding results concerning the inverse problem for the corresponding hyperbolic equation w tt = w ? qw. This is then reduced to use of the response to a singl...

In this chapter, a new family of multifactorial function, called generalized additive weighted multifactorial function, is proposed and discussed in detail. First, its properties in n-dimensional space are discussed and then our results are extended to the infinite dimensional space. Second, the implication of its constant coefficients is explained by fuzzy integral. Finally, its application in...