Related papers: A two-dimensional metric temporal logic
We consider Minkowski spacetime, the set of all point-events of spacetime under the relation of causal accessibility. That is, ${\sf x}$ can access ${\sf y}$ if an electromagnetic or (slower than light) mechanical signal could be sent from…
Verification of temporal logic properties plays a crucial role in proving the desired behaviors of continuous systems. In this paper, we propose an interval method that verifies the properties described by a bounded signal temporal logic.…
In this paper we present various temporal justification logics involving both past and future time modalities. We combine Artemov's logic of proofs with linear temporal logic (with both past and future operators), and establish its…
In this paper we consider the specification and verification of infinite-state systems using temporal logic. In particular, we describe parameterised systems using a new variety of first-order temporal logic that is both powerful enough for…
In temporal extensions of Answer Set Programming (ASP) based on linear-time, the behavior of dynamic systems is captured by sequences of states. While this representation reflects their relative order, it abstracts away the specific times…
In continuous logic, there are plenty of examples of interesting stable metric structures. However, on the other side of the SOP line, there are only a few metric structures where order is relevant, and orders often appear in different…
Formalisms based on temporal logics interpreted over finite strict linear orders, known in the literature as finite traces, have been used for temporal specification in automated planning, process modelling, (runtime) verification and…
We present two deductively equivalent calculi for non-deterministic many-valued logics. One is defined by axioms and the other - by rules of inference. The two calculi are obtained from the truth tables of the logic under consideration in a…
Recently, a thermodynamic definition of time has been introduced. This definition is useful to find approach some open problems in physics. But, it was obtained by a phenomenological approach and a logical inconsistency appears in the…
Our manuscript studies linear temporal (with UNTIL and NEXT) logic based at a conception of intransitive time. non-transitive time. In particular, we demonstrate how the notion of knowledge might be represented in such a framework (here we…
Temporal epistemic logic is a well-established framework for expressing agents knowledge and how it evolves over time. Within language-based security these are central issues, for instance in the context of declassification. We propose to…
We consider spacetime to be a 4-dimensional differentiable manifold that can be split locally into time and space. No metric, no linear connection are assumed. Matter is described by classical fields/fluids. We distinguish electrically…
We present the proof that the temporal logic of two-dimensional Minkowski spacetime is decidable, PSPACE-complete. The proof is based on a type of two-dimensional mosaic. Then we present the modification of the proof so as to work for…
Whereas standard treatments of temporal logic are adequate for closed systems, having no run-time interactions with their environment, they fall short for reactive systems, interacting with their environments through synchronisation of…
We introduce a temporal model for reasoning on disjunctive metric constraints on intervals and time points in temporal contexts. This temporal model is composed of a labeled temporal algebra and its reasoning algorithms. The labeled…
Linear topological spaces with partial ordering (linear kinematics) are studied. They are defined by a set of 8 axioms implying that topology, linear structure and ordering are compatible with each other. Most of the results are valid for…
We describe a general approach to deriving linear-time logics for a wide variety of state-based, quantitative systems, by modelling the latter as coalgebras whose type incorporates both branching and linear behaviour. Concretely, we define…
Temporal logics over finite traces have recently seen wide application in a number of areas, from business process modelling, monitoring, and mining to planning and decision making. However, real-life dynamic systems contain a degree of…
Temporal logics over finite traces are not the same as temporal logics over potentially infinite traces. Ro\c{s}u first proved completeness for linear temporal logic on finite traces (LTLf) with a novel coinductive axiom. We offer a…
Autonomous systems embedded with machine learning modules often rely on deep neural networks for classifying different objects of interest in the environment or different actions or strategies to take for the system. Due to the…