We present a syntactical cut-elimination proof for an extended sequent calculus covering the classical modal logics in the \(\mathsf{K}\), \(\mathsf{D}\), \(\mathsf{T}\), \(\mathsf{K4}\), \(\mathsf{D4}\) and \(\mathsf{S4}\) spectrum. We design the systems uniformly since they all share the same set of rules. Different logics are obtained by “tuning” a single parameter, namely a constraint on the applicability of the cut rule and on the (left and right, respectively) rules for \(\Box\) and \(\Diamond\). Starting points for this research are 2-sequents and indexed-based calculi (...) (sequents and tableaux). By extending and modifying existing proposals, we show how to achieve a syntactical proof of the cut-elimination theorem that is as close as possible to the one for first-order classical logic. In doing this, we implicitly show how small is the proof-theoretical distance between classical logic and the systems under consideration. (shrink)

We propose a natural deduction calculus for the modal logic S4.2. The system is designed to match as much as possible the structure and the properties of the standard system of natural deduction for first-order classical logic, exploiting the formal analogy between modalities and quantifiers. The system is proved sound and complete with respect to (w.r.t.) the standard Hilbert-style formulation of S4.2. Normalization and its consequences are obtained in a natural way, with proofs that closely follow the analogous ones for (...) first-order logic. (shrink)

We present a sequent calculus for the modal logic S4, and building on some relevant features of this system we show how S4 can easily be translated into full propositional linear logic, extending the Grishin-Ono translation of classical logic into linear logic. The translation introduces linear modalities only in correspondence with S4 modalities. We discuss the complexity of the decision problem for several classes of linear formulas naturally arising from the proposed translations.

The meaning of a formula built out of proof-functional connectives depends in an essential way upon the intensional aspect of the proofs of the component subformulas. We study three such connectives, strong equivalence (where the two directions of the equivalence are established by mutually inverse maps), strong conjunction (where the two components of the conjunction are established by the same proof) and relevant implication (where the implication is established by an identity map). For each of these connectives we give a (...) type assignment system, a realizability semantics, and a completeness theorem. This form of completeness implies the semantic completeness of the type assignment system. (shrink)

This workshop on stochastic theory and adaptive control assembled many of the leading researchers on stochastic control and stochastic adaptive control to increase scientific exchange and cooperative research between these two subfields of stochastic analysis. The papers included in the proceedings include survey and research. They describe both theoretical results and applications of adaptive control. There are theoretical results in identification, filtering, control, adaptive control and various other related topics. Some applications to manufacturing systems, queues, networks, medicine and other topics (...) are gien. (shrink)