This paper proposes a specification language, hybrid projection temporal logic of modelling, analyzing and verifying biological systems which can be considered, in general, to be hybrid systems consisting of a non-trivial mixture of discrete and continuous components. The syntax and semantics of the logic are presented, and some examples of hybrid systems are modelled to illustrate the formalism.

In this paper, we show how model-checking can be generalized to temporal logic constraint solving, by considering temporal logic formulae with free variables over some domain D, and by computing a validity domain for the variables rather than a truth value for the formula. This allows us to de ne a continuous degree of satisfaction for a temporal logic formula in a given structure, opening up t...

Continuous-time Markov chains (CTMCs) have been widely used to determine system performance and dependability characteristics. Their analysis most often concerns the computation of steady-state and transient-state probabilities. This paper introduces a branching temporal logic for expressing real-time probabilistic properties on CTMCs and presents approximate model checking algorithms for this ...

The concept of logic proposition induced functions is proposed in the present paper, then the concept of relative truth degree of propositions with respect to a logic theory Γ is introduced by means of infinite product of evenly distributed probability spaces and integrated semantics respectively w.r.t. discrete and continuous situations, and a graded approximate reasoning theory is established...

The increasing need for real time robotic systems capable of performing tasks in changing and constrained environments demands the development of reliable and adaptable motion planning and control algorithms. This paper considers a mobile robot whose performance is measured by the completion of temporal logic tasks within a certain period of time. In addition to such time constraints, the plann...

Article history: Received 15 July 2007 Revised 8 May 2008 Available online 11 October 2008 Thecommonmetric temporal logic for continuous timewereshowntobe insufficient,when it was proved that they cannot express a modality suggested by Pnueli. Moreover no finite temporal logic can express all the natural generalizations of this modality. It followed that if we look for an optimal decidable metr...

Using the theory of coalgebra, we introduce a uniform framework for adding modalities to language propositional geometric logic. Models this logic are based on coalgebras an endofunctor some full subcategory category topological spaces and continuous functions. We investigate derivation systems, soundness completeness such modal logics, specify method lifting Set, accompanied by collection pred...

We introduce a new formal logic, called equality propositional logic. It has two basic connectives, $boldsymbol{wedge}$ (conjunction) and $equiv$ (equivalence). Moreover, the $Rightarrow$ (implication) connective can be derived as $ARightarrow B:=(Aboldsymbol{wedge}B)equiv A$. We formulate the equality propositional logic and demonstrate that the resulting logic has reasonable properties such a...

this paper deals with continuous frames and continuous riesz bases. we introduce continuous riesz bases and give some equivalent conditions for a continuous frame to be a continuous riesz basis. it is certainly possible for a continuous frame to have only one dual. such a continuous frame is called a riesz-type frame [13]. we show that a continuous frame is riesz-type if and only if it is a con...