Related papers: Uniform Interpolation for Propositional and Modal …
Representation of classical dynamics by unitary transformations has been used to develop unified description of hybrid classical-quantum systems with particular type of interaction, and to formulate abstract systems interpolating between…
We study the mathematical properties of bilateral state-based modal logic (BSML), a modal logic employing state-based semantics (also known as team semantics), which has been used to account for free choice inferences and related linguistic…
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…
In this paper we show how the theory of monads can be used to deduce in a uniform manner several duality theorems involving categories of relations on one side and categories of algebras with homomorphisms preserving only some operations on…
We study hidden-variable models from quantum mechanics, and their abstractions in purely probabilistic and relational frameworks, by means of logics of dependence and independence, based on team semantics. We show that common desirable…
An approach to universal (meta-)logical reasoning in classical higher-order logic is employed to explore and study simplifications of Kurt G\"odel's modal ontological argument. Some argument premises are modified, others are dropped, modal…
Classical probability theory is formulated using sets. In this paper, we extend classical probability theory with propositional computability logic. Unlike other formalisms, computability logic is built on the notion of events/games, which…
We study interpolation properties for Shavrukov's bimodal logic $\mathbf{GR}$ of usual and Rosser provability predicates. For this purpose, we introduce a new sublogic $\mathbf{GR}^\circ$ of $\mathbf{GR}$ and its relational semantics. Based…
We study the underlying mathematical properties of various partial order models of concurrency based on transition systems, Petri nets, and event structures, and show that the concurrent behaviour of these systems can be captured in a…
Isomorphism between formulae is defined with respect to categories formalizing equality of deductions in classical propositional logic and in the multiplicative fragment of classical linear propositional logic caught by proof nets. This…
We study the relative succinctness and expressiveness of modal logics, and prove that these relationships can be as complex as any countable partial order. For this, we use two uniform formalisms to define modal operators, and obtain…
Unimodularity is localized to a complete stationary type, and its properties are analysed. Some variants of unimodularity for definable and type-definable sets are introduced, and the relationship between these different notions is studied.…
Classical logics of knowledge and belief are usually interpreted on Kripke models, for which a mathematically well-developed model theory is available. However, such models are inadequate to capture dynamic phenomena. Therefore, epistemic…
We investigate the properties of Inclusion Logic, that is, First Order Logic with Team Semantics extended with inclusion dependencies. We prove that Inclusion Logic is equivalent to Greatest Fixed Point Logic, and we prove that all…
We study whether a logic based on team semantics can be enriched with a conditional satisfying minimal requirements--namely, preservation of the closure property of the logic, Modus Ponens, and the Deduction Theorem. We show that such…
We study quantifiers and interpolation properties in \emph{orthologic}, a non-distributive weakening of classical logic that is sound for formula validity with respect to classical logic, yet has a quadratic-time decision procedure. We…
Generalized topological spaces are not necessarily closed under finite intersections. Moreover, the whole universe does not need to be open. We use modified version of this framework to establish certain models for non-normal modal logics.…
It is well known that dependence logic captures the complexity class NP, and it has recently been shown that inclusion logic captures P on ordered models. These results demonstrate that team semantics offers interesting new possibilities…
We prove a number of results motivated by global questions of uniformity in computability theory, and universality of countable Borel equivalence relations. Our main technical tool is a game for constructing functions on free products of…
Several notions of bisimulation relations for probabilistic non-deterministic transition systems have been considered in the literature. We consider a novel testing-based behavioral equivalence called upper-expectation bisimilarity and…