Related papers: The propositional logic of teams
Team semantics is the mathematical basis of modern logics of dependence and independence. In contrast to classical Tarski semantics, a formula is evaluated not for a single assignment of values to the free variables, but on a set of such…
We classify the computational complexity of the satisfiability, validity and model-checking problems for propositional independence, inclusion, and team logic. Our main result shows that the satisfiability and validity problems for…
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…
Modern logics of dependence and independence are based on team semantics, which means that formulae are evaluated not on a single assignment of values to variables, but on a set of such assignments, called a team. This leads to high…
We study the complexity of reasoning tasks for logics in team semantics. Our main focus is on the data complexity of model checking but we also derive new results for logically defined counting and enumeration problems. Our approach is…
We advance a doxastic interpretation for many of the logical connectives considered in Dependence Logic and in its extensions, and we argue that Team Semantics is a natural framework for reasoning about beliefs and belief updates.
We develop a denotational semantics of Linear Logic with least and greatest fixed points in coherence spaces (where both fixed points are interpreted in the same way) and in coherence spaces with totality (where they have different…
We introduce relational semantics for "flat Heyting-Lewis logic" $\mathsf{HLC}^{\flat}$. This logic arises as the extension of intuitionistic logic with a Lewis-style strict implication modality that, contrary to its "sharp" counterpart…
We introduce propositional team-based logics expressively complete for (quasi) downward and (quasi) upward closed properties in a syntactically dual way, by using variants of the inclusion atom. In particular, the variants of the primitive…
Logics with team semantics provide alternative means for logical characterization of complexity classes. Both dependence and independence logic are known to capture non-deterministic polynomial time, and the frontiers of tractability in…
We prove expressive completeness results for convex propositional and modal team logics, where a logic is convex if, for each formula, if it is true in two teams $t$ and $u$ and $t\subseteq s\subseteq u$, then it is also true in $s$. We…
We introduce some new logics of imperfect information by adding atomic formulas corresponding to inclusion and exclusion dependencies to the language of first order logic. The properties of these logics and their relationships with other…
We classify all apartness relations definable in propositional logics extending intuitionistic logic using Heyting algebra semantics. We show that every Heyting algebra which contains a non-trivial apartness term satisfies the weak law of…
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…
In this paper, we study several propositional team logics that are closed under unions, including propositional inclusion logic. We prove that all these logics are expressively complete, and we introduce sound and complete systems of…
In this paper, we propose a relational semantics of propositional language, which unifies the relational semantics of intuitionistic logic, Visser's Basic Propositional Logic and orthologic. Working in language $\{\bot,\land,\neg\}$ and…
We show that first-order logic can be translated into a very simple and weak logic, and thus set theory can be formalized in this weak logic. This weak logical system is equivalent to the equational theory of Boolean algebras with three…
We extend description logics (DLs) with non-monotonic reasoning features. We start by investigating a notion of defeasible subsumption in the spirit of defeasible conditionals as studied by Kraus, Lehmann and Magidor in the propositional…
Epistemic logics of intensional groups lift the assumption that membership in a group of agents is common knowledge. Instead of being represented directly as a set of agents, intensional groups are represented by a property that may change…
This paper presents a new system of logic, LF, that is intended to be used as the foundation of the formalization of science. That is, deductive validity according to LF is to be used as the criterion for assessing what follows from the…