ABSTRACT We introduce a two-dimensional temporal logic as a formalism which enables the description of both the history of a world and the evolution of an observer's views about the history. We apply such formalism to the description of certain problems that occur in historical database systems due to updates. The historical dimension describes the history of a world according to an observer's view at a certain moment in time. The transaction dimension describes the evolution of an observer's view; changes (...) can occur in the observer's view of the present and future as well as in his views of the past. The database is seens as an observer of the history of the world. Besides describing the history of the world, the database system can also execute temporal specifications in the form of temporal actions. The two-dimensional formalism is used to describe the effects of updates in the execution of temporal actions. The detection of some problematic effects and its implementation are discussed. (shrink)

Let $\mathcal{L}$ be a propositional language with standard Boolean connectives plus two modalities: an S4-ish topological modality $\square$ and a temporal modality $\bigcirc$ , understood as ‘next’. We extend the topological semantic for S4 to a semantics for the language $\mathcal{L}$ by interpreting $\mathcal{L}$ in dynamic topological systems, i.e. ordered pairs $\langle X, f\rangle$ , where X is a topological space and f is a continuous function on X. Artemov, Davoren and Nerode have axiomatized a logic S4C, and have shown (...) that S4C is sound and complete for this semantics. Zhang and Mints have shown that S4C is complete relative to a particular topological space, Cantor space. The current paper produces an alternate proof of the Zhang-Mints result. (shrink)

Model checking is a widely used technique that aids in the designand debugging of reactive systems. This paper gives an overview onthe theory and algorithms used for model checking, with a biastowards automata-theoretic approaches and linear-time temporallogic. We also describe elementary abstraction techniques useful forlarge systems that cannot be directly handled by model checking.

Until is a notoriously difficult temporal operator as it is both existential and universal at the same time: A∪B holds at the current time instant w iff either B holds at w or there exists a time instant w' in the future at which B holds and such that A holds in all the time instants between the current one and ẃ. This “ambivalent” nature poses a significant challenge when attempting to give deduction rules for until. In this paper, in (...) contrast, we make explicit this duality of until by introducing a new temporal operator ∇ that allows us to formalize the “history” of until, i.e., the “internal” universal quantification over the time instants between the current one and ẃ. This approach provides the basis for formalizing deduction systems for temporal logics endowed with the until operator. For concreteness, we give here a labeled natural deduction system N(LTL∇) for a linear-time logic LTL∇ endowed with the new history operator. We show that LTL∇ is equivalent to the linear temporal logic LTL with until, which follows by formalizing back and forth translations between the two logics. We also define an indirect translation from LTL∇ into LTL via temporal logics with past operators; such a result provides an upper bound to the problem of satisfiability for LTL∇ formulas. (shrink)

modality , understood as ‘next’. We extend the topological semantic for S4 to a semantics for the language L by interpreting L in dynamic topological systems, i.e. ordered pairs X, f , where X is a topological space and f is a..

We study the formal first order system TIND in the standard language of Gentzen's LK . TIND extends LK by the purely logical rule of term-induction, that is a restricted induction principle, deriving numerals instead of arbitrary terms. This rule may be conceived as the logical image of full induction.