Related papers: Hierarchies in Dependence Logic
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…
We introduce a universal algebraic generalization of de Jongh's notion of dependence for formulas of intuitionistic propositional logic, relating it to a notion of dependence defined by Marczewski for elements of an algebraic structure.…
We present a type theory combining both linearity and dependency by stratifying typing rules into a level for logics and a level for programs. The distinction between logics and programs decouples their semantics, allowing the type system…
Modern categorical logic as well as the Kripke and topological models of intuitionistic logic suggest that the interpretation of ordinary "propositional" logic should in general be the logic of subsets of a given universe set. Partitions on…
Separation logic and its variants can describe various properties on pointer programs. However, when it comes to properties on sequences, one may find it hard to formalize. To deal with properties on variable-length sequences and multilevel…
A type theory is presented that combines (intuitionistic) linear types with type dependency, thus properly generalising both intuitionistic dependent type theory and full linear logic. A syntax and complete categorical semantics are…
We contribute to the refined understanding of the language-logic-algebra interplay in the context of first-order properties of countable words. We establish decidable algebraic characterizations of one variable fragment of FO as well as…
An ordinal view of independence is studied in the framework of possibility theory. We investigate three possible definitions of dependence, of increasing strength. One of them is the counterpart to the multiplication law in probability…
Separation Logic is a widely used formalism for describing dynamically allocated linked data structures, such as lists, trees, etc. The decidability status of various fragments of the logic constitutes a long standing open problem. Current…
We study dependence and independence concepts found in quantum physics, especially those related to hidden variables and non-locality, through the lens of team semantics and probabilistic team semantics, adapting a relational framework…
Categorical Universal Logic is a theory of monad-relativised hyperdoctrines (or fibred universal algebras), which in particular encompasses categorical forms of both first-order and higher-order quantum logics as well as classical,…
Inquisitive team logic is a variant of inquisitive logic interpreted in team semantics, which has been argued to provide a natural setting for the regimentation of dependence claims. With respect to sentences, this logic is known to be…
We study a natural hierarchy in first-order logic, namely the quantifier structure hierarchy, which gives a systematic classification of first-order formulas based on structural quantifier resource. We define a variant of…
In this paper we study the expressive power of Horn-formulae in dependence logic and show that they can express NP-complete problems. Therefore we define an even smaller fragment D-Horn* and show that over finite successor structures it…
Intuitionistic dependence logic was introduced by Abramsky and Vaananen (2009) as a variant of dependence logic under a general construction of Hodges' (trump) team semantics. It was proven that there is a translation from intuitionistic…
We prove that the expressive power of first-order logic with team semantics plus contradictory negation does not rise beyond that of first-order logic (with respect to sentences), and that the totality atoms of arity k +1 are not definable…
We present role logic, a notation for describing properties of relational structures in shape analysis, databases, and knowledge bases. We construct role logic using the ideas of de Bruijn's notation for lambda calculus, an encoding of…
We examine the relationship between Dependence Logic and game logics. A variant of Dynamic Game Logic, called Transition Logic, is developed, and we show that its relationship with Dependence Logic is comparable to the one between…
Modal logic is a paradigm for several useful and applicable formal systems in computer science. It generally retains the low complexity of classical propositional logic, but notable exceptions exist in the domains of description, temporal,…
This article fits in the area of research that investigates the application of topological duality methods to problems that appear in theoretical computer science. One of the eventual goals of this approach is to derive results in…