Related papers: Abstract Effects and Proof-Relevant Logical Relati…
Dependently typed programs contain an excessive amount of static terms which are necessary to please the type checker but irrelevant for computation. To separate static and dynamic code, several static analyses and type systems have been…
We give a new formulation of Turing reducibility in terms of higher modalities, inspired by an embedding of the Turing degrees in the lattice of subtoposes of the effective topos discovered by Hyland. In this definition, higher modalities…
We describe a Martin-L\"of-style dependent type theory, called Cocon, that allows us to mix the intensional function space that is used to represent higher-order abstract syntax (HOAS) trees with the extensional function space that…
This paper presents a simple decidable logic of functional dependence LFD, based on an extension of classical propositional logic with dependence atoms plus dependence quantifiers treated as modalities, within the setting of generalized…
We consider logic-based argumentation in which an argument is a pair (Fi,al), where the support Fi is a minimal consistent set of formulae taken from a given knowledge base (usually denoted by De) that entails the claim al (a formula). We…
In this work we propose a multi-valued extension of logic programs under the stable models semantics where each true atom in a model is associated with a set of justifications, in a similar spirit than a set of proof trees. The main…
In recent years, the logic of questions and dependencies has been investigated in the closely related frameworks of inquisitive logic and dependence logic. These investigations have assumed classical logic as the background logic of…
Defeasible reasoning is a simple but efficient approach to nonmonotonic reasoning that has recently attracted considerable interest and that has found various applications. Defeasible logic and its variants are an important family of…
Type and effect systems are a tool to analyse statically the behaviour of programs with effects. We present a proof based on the so called reducibility candidates that a suitable stratification of the type and effect system entails the…
We propose a novel ranking-based semantics for Dung-style argumentation frameworks with the help of conditional logics. Using an intuitive translation for an argumentation framework to generate conditionals, we can apply nonmonotonic…
We explain how recent developments in the fields of realisability models for linear logic -- or geometry of interaction -- and implicit computational complexity can lead to a new approach of implicit computational complexity. This…
\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…
We extend the {\lambda}-calculus with constructs suitable for relational and functional-logic programming: non-deterministic choice, fresh variable introduction, and unification of expressions. In order to be able to unify…
We introduce proper display calculi for basic monotonic modal logic,the conditional logic CK and a number of their axiomatic extensions. These calculi are sound, complete, conservative and enjoy cut elimination and subformula property. Our…
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…
Stereotypical reasoning assumes that the situation at hand is one of a kind and that it enjoys the properties generally associated with that kind of situation. It is one of the most basic forms of nonmonotonic reasoning. A formal model for…
The language of epistemic specifications and epistemic logic programs extends disjunctive logic programs under the stable model semantics with modal constructs called subjective literals. Using subjective literals, it is possible to check…
We develop a model of abduction in abstract argumentation, where changes to an argumentation framework act as hypotheses to explain the support of an observation. We present dialogical proof theories for the main decision problems (i.e.,…
The study of causal abstractions bridges two integral components of human intelligence: the ability to determine cause and effect, and the ability to interpret complex patterns into abstract concepts. Formally, causal abstraction frameworks…
Given the large variety of existing logical formalisms it is of utmost importance to select the most adequate one for a specific purpose, e.g. for representing the knowledge relevant for a particular application or for using the formalism…