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The language of probability is used to define several different types of conditional statements. There are four principal types: subjunctive, material, existential, and feasibility. Two further types of conditionals are defined using the…
Our understanding about things is conceptual. By stating that we reason about objects, it is in fact not the objects but concepts referring to them that we manipulate. Now, so long just as we acknowledge infinitely extending notions such as…
Description logics are a powerful tool for describing ontological knowledge bases. That is, they give a factual account of the world in terms of individuals, concepts and relations. In the presence of uncertainty, such factual accounts are…
Many forms of dependence manifest themselves over time, with behavior of variables in dynamical systems as a paradigmatic example. This paper studies temporal dependence in dynamical systems from a logical perspective, by enriching a…
We extend the usual internal logic of a (pre)topos to a more general interpretation, called the stack semantics, which allows for "unbounded" quantifiers ranging over the class of objects of the topos. Using well-founded relations inside…
It is demonstrated that under the hypothesis of boundedness, the semantics appears as a property of spontaneous physical processes. It turns that both semantic structure and semantic meaning have their own physical agents each of which is…
We tackle the problem of conditioning probabilistic programs on distributions of observable variables. Probabilistic programs are usually conditioned on samples from the joint data distribution, which we refer to as deterministic…
This paper establishes and proves representation theorems for cumulative propositional dependence logic and for cumulative propositional logic with team semantics. Cumulative logics are famously given by System C. For propositional…
A central concept within informatics is in modelling such systems for the purpose of reasoning (perhaps automated) about their behaviour and properties. To this end, one requires an interpretation of logical formulae in terms of the…
Possibilistic logic has been proposed as a numerical formalism for reasoning with uncertainty. There has been interest in developing qualitative accounts of possibility, as well as an explanation of the relationship between possibility and…
We developed a type-theoretical framework for natural lan- guage semantics that, in addition to the usual Montagovian treatment of compositional semantics, includes a treatment of some phenomena of lex- ical semantic: coercions, meaning,…
In this paper, we introduce a logic based on team semantics, called FOT, whose expressive power is elementary, i.e., coincides with first-order logic both on the level of sentences and (possibly open) formulas, and we also show that a…
In systems modelling, a 'system' typically comprises located resources relative to which processes execute. One important use of logic in informatics is in modelling such systems for the purpose of reasoning (perhaps automated) about their…
The study of group knowledge concepts such as mutual, common, and distributed knowledge is well established within the discipline of epistemic logic. In this work, we incorporate epistemic abilities of agents to refine the formal definition…
We present Lilac, a separation logic for reasoning about probabilistic programs where separating conjunction captures probabilistic independence. Inspired by an analogy with mutable state where sampling corresponds to dynamic allocation, we…
We extend the framework of abstract algebraic logic to weak logics, namely logical systems which are not necessarily closed under uniform substitution. We interpret weak logics by algebras expanded with an additional predicate and we…
The languages of logics based on team semantics typically only allow atomic negation or restricted negation. In this paper, we explore propositional team-based logics with full (intuitionistic) negation. We demonstrate that including full…
The mathematical representation of semantics is a key issue for Natural Language Processing (NLP). A lot of research has been devoted to finding ways of representing the semantics of individual words in vector spaces. Distributional…
This paper belongs to the field of probabilistic modal logic, focusing on a comparative analysis of two distinct semantics: one rooted in Kripke semantics and the other in neighbourhood semantics. The primary distinction lies in the…
In this work, we want to give an overview on which pragmatic abilities have been tested in LLMs so far and how these tests have been carried out. To do this, we first discuss the scope of the field of pragmatics and suggest a subdivision…