Related papers: Normalisation for Some Infectious Logics and Their…
This article initiates the semantic study of distribution-free normal modal logic systems, laying the semantic foundations and anticipating further research in the area. The article explores roughly the same area, though taking a different…
Drawing appropriate defeasible inferences has been proven to be one of the most pervasive puzzles of natural language processing and a recurrent problem in pragmatics. This paper provides a theoretical framework, called ``stratified…
In real-world applications, knowledge bases consisting of all the information at hand for a specific domain, along with the current state of affairs, are bound to contain contradictory data coming from different sources, as well as data…
Problems in two axiomatizations of Ja\'skowski's discussive (or discursive) logic D2 are considered. A recent axiomatization of D2 and completeness proof relative to D2's intended semantics seems to be mistaken because some formulas valid…
Recent technological advances have led to unprecedented amounts of generated data that originate from the Web, sensor networks and social media. Analytics in terms of defeasible reasoning - for example for decision making - could provide…
Different theorem provers tend to produce proof objects in different formats and this is especially the case for modal logics, where several deductive formalisms (and provers based on them) have been presented. This work falls within the…
We consider a modal logic that can formalise statements about uncertainty and beliefs such as `I think that my wallet is in the drawer rather than elsewhere' or `I am confused whether my appointment is on Monday or Tuesday'. To do that, we…
Abstraction logic is a new logic, serving as a foundation of mathematics. It combines features of both predicate logic and higher-order logic: abstraction logic can be viewed both as higher-order logic minus static types as well as…
Undulation of infection levels, usually called waves, are not well understood. In this paper we propose a mathematical model that exhibits undulation and decay towards a stable state. The model is a re-interpretation of the original…
The skew monoidal categories of Szlach\'anyi are a weakening of monoidal categories where the three structural laws of left and right unitality and associativity are not required to be isomorphisms but merely transformations in a particular…
We consider the question of extending propositional logic to a logic of plausible reasoning, and posit four requirements that any such extension should satisfy. Each is a requirement that some property of classical propositional logic be…
We prove normalization for (univalent, Cartesian) cubical type theory, closing the last major open problem in the syntactic metatheory of cubical type theory. Our normalization result is reduction-free, in the sense of yielding a bijection…
We further develop the abstract algebraic logic approach to input/output logic initiated in \cite{wollic22}, where the family of selfextensional logics was proposed as a general background environment for input/output logics. In this paper,…
Refining and extending previous work by Retor\'e, we develop a systematic approach to intersection types via natural deduction. We show how a step of beta reduction can be seen as performing, at the level of typing derivations, Prawitz…
I derive a Wick ordered continuous renormalization group equation for fermion systems and show that a determinant bound applies directly to this equation. This removes factorials in the recursive equation for the Green functions, and thus…
These are notes on discrete mathematics for computer scientists. The presentation is somewhat unconventional. Indeed I begin with a discussion of the basic rules of mathematical reasoning and of the notion of proof formalized in a natural…
Deduction systems and graph rewriting systems are compared within a common categorical framework. This leads to an improved deduction method in diagrammatic logics.
The proof theory and semantics of intuitionistic modal logics have been studied by Simpson in terms of Prawitz-style labelled natural deduction systems and Kripke models. An alternative to model-theoretic semantics is provided by…
We introduce a logic for knowledge representation and reasoning on protein-protein interactions. Modulo a theory, formulas describe protein structures and dynamic changes. They can be composed in order to add or remove static and dynamic…
Justification logics are modal-like logics with the additional capability of recording the reason, or justification, for modalities in syntactic structures, called justification terms. Justification logics can be seen as explicit…