Duration Calculus (DC) is a real-time logic with measurement of duration of propositions in observation intervals. It is a highly expressive logic with continuous time behaviours (also called signals) as its models. Validity checking of DC is undecidable. We propose a method for validity checking of Duration Calculus by reduction to a sampled time version of this logic called well sampled Inter...

This paper investigates the motion planning of autonomous dynamical systems modeled by Markov decision processes (MDP) with unknown transition probabilities over continuous state and action spaces. Linear temporal logic (LTL) is used to specify high-level tasks infinite horizon, which can be converted into a limit deterministic generalized B\"uchi automaton (LDGBA) several accepting sets. The n...

We develop several aspects of local and global stability in continuous first order logic. In particular, we study type-definable groups and genericity.

Considering different implication operators, such as Lukasiewicz, Gödel or product implication in the same logic program, naturally leads to the allowance of several adjoint pairs in the lattice of truthvalues. In this paper we apply this idea to introduce multi-adjoint logic programs as an extension of monotonic logic programs. The continuity of the immediate consequences operators is proved a...

In the last 15 years, research in Computer Science has involved many paradigms in which continuous time appears whether in a pure way or in cooperation with discrete time. In particular, this is evident in subjects concerning Automata and Logic. This issue of FI consists of four papers dedicated to such subjects. The papers will be referred to below as [HR], [S], [PRT], [T] (the initials of the...

This paper shows that a classic metalogical framework, including all Boolean operators, can be used to support the development of a metric behavioural theory for Markov processes. Previously, only intuitionistic frameworks or frameworks without negation and logical implication have been developed to fulfill this task. The focus of this paper is on continuous Markovian logic (CML), a logic that ...

We investigate an open question concerning properties of algebraic independence in continuous theories (see Section 4). The rest of the work is essentially a translation to continuous logic of popular notions of independence (in particular, forking and dividing). Much of the time we are simply “copying” classical proofs from well-known sources, while along the way making the necessary adjustmen...

This paper presents a new concept of continuous-valued logic (Multi level logic) (CVL) which can be applied to control the pulse width of an internally generated PWM in a microcontroller. The input threshold voltage controls duty cycle of generated PWM. The basis of continuous-valued logic (CVL) relies on the unstable generated oscillation of a digital output where the program referred non-Schm...