Related papers: Elementwise semantics in categories with pull-back…
The paper explores applications of Kripke's theory of truth to semantics for anti-luck epistemology, that is, to subjunctive theories of knowledge. Subjunctive theories put forward modal or subjunctive conditions to rule out knowledge by…
This work extends Halpern and Pearl's causal models for actual causality to a possible world semantics environment. Using this framework we introduce a logic of actual causality with modal operators, which allows for reasoning about…
Due to the increased complexity of software development projects more and more systems are described by models. The sheer size makes it impractical to describe these systems by a single model. Instead many models are developed that provide…
In this paper, we introduce a new family of argument-ranking semantics which can be seen as a refinement of the classification of arguments into skeptically accepted, credulously accepted and rejected. To this end we use so-called social…
To any left system of diagram categories or to any left pointed derivateur (in the sense of Grothendieck) a K-theory space is associated. This K-theory space is shown to be canonically an infinite loop space and to have a lot of common…
Probabilistic argumentation allows reasoning about argumentation problems in a way that is well-founded by probability theory. However, in practice, this approach can be severely limited by the fact that probabilities are defined by adding…
Category Theory provides us with a clear notion of what is an internal structure. This will allow us to focus our attention on a certain type of relationship between context and structure.
As the prototypical category, $\mathbf{Set}$ has many properties which make it special amongst categories. From the point of view of mathematical logic, one such property is that $\mathbf{Set}$ has enough structure to "properly" formalise…
The purpose of this book is to lay out certain aspects of descriptive set theory. After initially establishing notation and generalities we proceed to the following topics: partitions, semirings, rings, $\sigma$-rings, $\delta$-rings,…
The theory of random attractors has different notions of attraction, amongst them pullback attraction and weak attraction. We investigate necessary and sufficient conditions for the existence of pullback attractors as well as of weak…
Justification theory is a unifying framework for semantics of non-monotonic logics. It is built on the notion of a justification, which intuitively is a graph that explains the truth value of certain facts in a structure. Knowledge…
Given a group, we construct a fundamental additive functor on its orbit category. We prove that any isomorphism conjecture valid for this fundamental isomorphism functor holds for all additive functors, like K-theory, cyclic homology,…
We reformulate recent advances in directed type theory--a type theory where the types have the structure of synthetic (higher) categories--as a logical calculus with multiple context 'zones', following the example of Pfenning and Davies.…
We introduce a notion of compatibility between constraint encoding and compositional structure. Phrased in the language of category theory, it is given by a "composable constraint encoding". We show that every composable constraint encoding…
We present some motivations and discuss various aspects of an approach to the Jacobian Conjecture in terms of irreducible elements and square-free elements.
Trace semantics has been defined for various kinds of state-based systems, notably with different forms of branching such as non-determinism vs. probability. In this paper we claim to identify one underlying mathematical structure behind…
We consider the space of $n$-tuples of pairwise commuting elements in the Lie algebra of $U(m)$. We relate its one-point compactification to the subquotients of certain rank filtrations of connective complex $K$-theory. We also describe the…
The concept of relative sectional category expands upon classical sectional category theory by incorporating the pullback of a fibration along a map. Our paper aims not only to explore this extension but also to thoroughly investigate its…
Categories of polymorphic lenses in computer science, and of open games in compositional game theory, have a curious structure that is reminiscent of compact closed categories, but differs in some crucial ways. Specifically they have a…
In this work we suggest the use of a set-theoretical interpretation of semantic tableaux for teaching propositional logic. If the student has previous notions of basic set theory, this approach to semantical tableaux can clarify her the way…