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A class of interval-based temporal languages for uniformly representing and reasoning about actions and plans is presented. Actions are represented by describing what is true while the action itself is occurring, and plans are constructed…
Logical formalisms provide a natural and concise means for specifying and reasoning about preferences. In this paper, we propose lexicographic logic, an extension of classical propositional logic that can express a variety of preferences,…
Motivated by questions like: which spatial structures may be characterized by means of modal logic, what is the logic of space, how to encode in modal logic different geometric relations, topological logic provides a framework for studying…
We start from two closure operators defined on the elements of a special kind of partially ordered sets, called causal nets. Causal nets are used to model histories of concurrent processes, recording occurrences of local states and of…
Human ability at solving complex tasks is helped by priors on object and event semantics of their environment. This paper investigates the use of similar prior knowledge for transfer learning in Reinforcement Learning agents. In particular,…
We present a first-order logic equipped with an "asymmetric" directed notion of equality, which can be thought of as rewrites between terms, allowing for types to be interpreted as preorders. The logic is equipped with a precise syntactic…
We consider a language together with the subword relation, the cover relation, and regular predicates. For such structures, we consider the extension of first-order logic by threshold- and modulo-counting quantifiers. Depending on the…
Using the tensor category theory developed by Lepowsky, Zhang and the second author, we construct a braided tensor category structure with a twist on a semisimple category of modules for an affine Lie algebra at an admissible level. We…
This paper introduces a logic with a class of social network models that is based on standard Linear Temporal Logic (LTL), leveraging the power of existing model checkers for the analysis of social networks. We provide a short literature…
Regular cost functions have been introduced recently as an extension to the notion of regular languages with counting capabilities, which retains strong closure, equivalence, and decidability properties. The specificity of cost functions is…
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…
\textbf{T-BAT} logic is a formal system designed to express the notion of informal provability. This type of provability is closely related to mathematical practice and is quite often contrasted with formal provability, understood as a…
Experts do not always feel very, comfortable when they have to give precise numerical estimations of certainty degrees. In this paper we present a qualitative approach which allows for attaching partially ordered symbolic grades to logical…
Linear Logic refines Intuitionnistic Logic by taking into account the resources used during the proof and program computation. In the past decades, it has been extended to various frameworks. The most famous are indexed linear logics which…
Tate's central extension originates from 1968 and has since found many applications to curves. In the 80s Beilinson found an n-dimensional generalization: cubically decomposed algebras, based on ideals of bounded and discrete operators in…
Dynamic Topological Logic ($\mathcal{DTL}$) is a combination of $\mathcal{S}${\em 4}, under its topological interpretation, and the temporal logic $\mathcal{LTL}$ interpreted over the natural numbers. $\mathcal{DTL}$ is used to reason about…
The well known operator ordering ambiguity could motivate the existence of generations. This possibility is explored by exploiting the relationship between ordering and discretization rules. Context is drawn from lattice theory and non…
The unification of logic and probability is a long-standing concern in AI, and more generally, in the philosophy of science. In essence, logic provides an easy way to specify properties that must hold in every possible world, and…
This note provides a pedagogical introduction to Langer's theory for activated rate processes in multiple dimensions at the high friction limit, with an emphasis on the connection between the theory and the property of the backward…
The language of linear temporal logic can be interpreted over the class of dynamic topological systems, giving rise to the intuitionistic temporal logic ${{\sf ITL}^{\sf c}}_{\Diamond,\forall}$, recently shown to be decidable by…