Related papers: Exploring the Jungle of Intuitionistic Temporal Lo…
Type-free systems of logic are designed to consistently handle significant instances of self-reference. Some consistent type-free systems also have the feature of allowing the sort of general abstraction or comprehension principle that…
The Kripke semantics of classical propositional normal modal logic is made algebraic via an embedding of Kripke structures into the larger class of pointed stably supported quantales. This algebraic semantics subsumes the traditional…
We introduce and develop a set-based semantics for asynchronous TeamLTL. We consider two canonical logics in this setting: the extensions of TeamLTL by the Boolean disjunction and by the Boolean negation. We establish fascinating…
Types in logic programming have focused on conservative approximations of program semantics by regular types, on one hand, and on type systems based on a prescriptive semantics defined for typed programs, on the other. In this paper, we…
LTL3 is a multi-valued variant of Linear-time Temporal Logic for runtime verification applications. The semantic descriptions of LTL3 in previous work are given only in terms of the relationship to conventional LTL. Our approach, by…
Intuitionistic grammar logics fuse constructive and multi-modal reasoning while permitting the use of converse modalities, serving as a generalization of standard intuitionistic modal logics. In this paper, we provide definitions of these…
Temporal logic inference is the process of extracting formal descriptions of system behaviors from data in the form of temporal logic formulas. The existing temporal logic inference methods mostly neglect uncertainties in the data, which…
In the literature, two powerful temporal logic formalisms have been proposed for expressing information flow security requirements, that in general, go beyond regular properties. One is classic, based on the knowledge modalities of…
The relationship between intuitionistic or intermediate logics and logic programming has been extensively studied, prominently featuring Pearce's equilibrium logic and Osorio's safe beliefs. Equilibrium logic admits a fixpoint…
We consider systems under uncertainty whose dynamics are partially unknown. Our aim is to study satisfaction of temporal logic properties by trajectories of such systems. We express these properties as signal temporal logic formulas and…
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…
The intuitionistic modal logics considered between Constructive K (CK) and Intuitionistic K (IK) differ in their treatment of the possibility (diamond) connective. It was recently rediscovered that some logics between CK and IK also…
We give a calculus for reasoning about the first-order fragment of classical logic that is adequate for giving the truth conditions of intuitionistic Kripke frames, and outline a proof-theoretic soundness and completeness proof, which we…
It is proposed that the theory of dynamical systems offers appropriate tools to model many phonological aspects of both speech production and perception. A dynamic account of speech rhythm is shown to be useful for description of both…
We develop a classical propositional logic for reasoning about combinatory logic. We define its syntax, axiomatic system and semantics. The syntax and axiomatic system are presented based on classical propositional logic, with typed…
We develop polytopological semantics for various constructive, intuitionistic, and G\"odel--Dummett variations of $\mathsf{K4}$ and $\mathsf{S4}$. In our models, intuitionistic and modal operators are interpreted via various topologies over…
Using recent results in topos theory, two systems of higher-order logic are shown to be complete with respect to sheaf models over topological spaces---so-called ``topological semantics''. The first is classical higher-order logic, with…
Argumentation is a very active research field of Artificial Intelligence concerned with the representation and evaluation of arguments used in dialogues between humans and/or artificial agents. Acceptability semantics of formal…
The abstraction introduced by von Neumann correctly reflected the state of the art 70 years ago. Although it omitted data transmission time between components of the computer, it served as an excellent base for classic computing for…
Commonsense temporal reasoning at scale is a core problem for cognitive systems. The correct inference of the duration for which fluents hold is required by many tasks, including natural language understanding and planning. Many AI systems…