It is known that Metric Temporal Logic (MTL) is strictly less expressive than the Monadic First-Order Logic of Order and Metric (FO[<,+1]) in the pointwise semantics over bounded time domains (i.e., timed words of bounded duration) [2]. In this paper, we present an extension of MTL, relying on two new temporal operators ‘Earlier’ (E) and ‘Newer’ (N), which has the same expressive power as FO[<,...

We deene a class of modal logics LF by uniformly extending a class of modal logics L. Each logic L is characterised by a class of rst-order deenable frames, but the corresponding logic LF is sometimes characterised by classes of modal frames that are not rst-order deenable. The class LF includes provability logics with deep arithmeti-cal interpretations. Using Belnap's proof-theoretical framewo...

In this paper, we study Boolean BI Logic (BBI) from a semantic perspective. This logic arises as a logical basis of some recent separation logics used for reasoning about mutable data structures and we aim at proposing new results from alternative semantic foundations for BBI that seem to be necessary in the context of modeling and proving program properties. Starting from a Kripke relational s...

We present a syntactic abstraction method to reason about first-order modal logics by using theorem provers for standard first-order logic and for propositional modal logic.

In this paper, a sequent calculus for a hybrid categorial type logic (HCTL) is obtained following Seligman’s internalization strategy (Seligman 2001). With this strategy, a sequent calculus for a hybrid language can be developed starting from a first order sequent calculus. Seligman exemplifies his strategy developing a calculus for hybrid modal logics, but rises the question of whether the str...

In this short note we discuss several perspectives on the notion of Guarded Fragments (GFs) of first-order logic first introduced by Andréka, van Benthem and Németi. We focus on computational aspects, discussing some applications of GFs together with issues like the design of effective decision methods for specific reasoning tasks and the role of GFs in explaining the general good behavior of m...

We introduce a multi-type display calculus for Propositional Dynamic Logic (PDL). This calculus is complete w.r.t. PDL, and enjoys Belnap-style cut-elimination and subformula property.

3 Equivalences, Modal and Temporal Logics 5 3.1 Interactive games and bisimulations . . . . . . . . . . . . . . . 7 3.2 Modal logic and bisimulations . . . . . . . . . . . . . . . . . . . 9 3.3 Temporal properties and modal mu-calculus . . . . . . . . . . 10 3.4 Second-order propositional modal logic . . . . . . . . . . . . . . 15 3.5 Fixed point and second-order games . . . . . . . . . . . . ....

The basic principles and results of Conservative Logic introduced by Fredkin and Toffoli in [FT, 82] on the basis of a seminal paper of Landauer [La, 61] are extended to d–valued logics, with a special attention to three–valued logics. Different approaches to d–valued logics are examined in order to determine some possible universal sets of logic primitives. In particular, we consider the typic...

Alternative proofs for Guaspari and Solovay's completeness theorems for R are presented. R is an extension of the provability logic L and was developed in order to study the formal properties of the provability predicate of PA occurring in sentences that may contain connectives for witness comparison. (The primary example of sentences involving witness comparison is the Rosser sentence.) In thi...