In this paper we study natural deduction for the intuitionistic and classical (normal) modal logics obtained from the combinations of the axioms T, B, 4 and 5. In this context we introduce a new multi-contextual structure, called T-sequent, that allows to design simple labelfree natural deduction systems for these logics. After proving that they are sound and complete we show that they satisfy the normalization property and consequently the subformula property in the intuitionistic case.

We propose a separation logic where resources are histories (sequences) of epistemic actions so that resource update means concatenation of histories and resource decomposition means splitting of histories. This separation logic, called AMHSL, allows us to reason about the past: does what is true now depend on what was true in the past, before certain actions were executed? We show that the multiplicative connectives can be eliminated from a logical language with also epistemic and action model modalities, if the horizon (...) of epistemic actions is bounded. (shrink)

In this paper we present an extension of (bunched) separation logic, Boolean BI, with epistemic and dynamic epistemic modalities. This logic, called action model separation logic ( \(\mathrm {AMSL}\) ), can be seen as a generalization of public announcement separation logic in which we replace public announcements with action models. Then we not only model public information change (public announcements) but also non-public forms of information change, such as private announcements. In this context the semantics for the connectives \(*\) and (...) \(\mathrel {-*}\) from separation logic are epistemic versions of their usual semantics. This is because formulas are interpreted in states, not in resources, and agents may be uncertain between different states representing the same resource. We present the logic \(\mathrm {AMSL}\) and its semantics, with a detailed case study that highlights its interest for modeling. We also prove the elimination of the dynamics modalities and discuss some alternative epistemic semantics for the separation connectives. (shrink)

Ce numéro spécial, édité à l’occasion du centenaire de la naissance d’Alan Turing, est le fruit d’une double collaboration : d’une part une collaboration internationale qui exprime via internet l’importance de l’année Turing, d’autre part une collaboration locale régulière entre des chercheurs de l’équipe TYPES du Laboratoire Lorrain de Recherche en Informatique (LORIA) qui s’intéressent à la logique, la théorie de la preuve et la programmation, et des philosophes et logiciens du Laboratoire...