Related papers: A van Benthem Theorem for Quantitative Probabilist…
In the style of Lindstr\"om's theorem for classical first-order logic, this article characterizes propositional bi-intuitionistic logic as the maximal (with respect to expressive power) abstract logic satisfying a certain form of…
Non-additive uncertainty theories, typically possibility theory, belief functions and imprecise probabilities share a common feature with modal logic: the duality properties between possibility and necessity measures, belief and…
We propose a logic for true concurrency whose formulae predicate about events in computations and their causal dependencies. The induced logical equivalence is hereditary history preserving bisimilarity, and fragments of the logic can be…
Modal interpretations have the ambition to construe quantum mechanics as an objective, man-independent description of physical reality. Their second leading idea is probabilism: quantum mechanics does not completely fix physical reality but…
Timed transition systems are behavioural models that include an explicit treatment of time flow and are used to formalise the semantics of several foundational process calculi and automata. Despite their relevance, a general mathematical…
A landmark result in the study of logics for formal verification is Janin & Walukiewicz's theorem, stating that the modal $\mu$-calculus ($\mu\mathrm{ML}$) is equivalent modulo bisimilarity to standard monadic second-order logic (here…
Uniform interpolation is the property that, for any formula and set of atoms, there exists the strongest consequence omitting those atoms. It plays a central role in knowledge representation and reasoning tasks such as knowledge update and…
We present a comparative study between classical probability and quantum probability from the Bayesian viewpoint, where probability is construed as our rational degree of belief on whether a given statement is true. From this viewpoint,…
Substructural logics naturally support a quantitative interpretation of formulas, as they are seen as consumable resources. Distances are the quantitative counterpart of equivalence relations: they measure how much two objects are similar,…
Larsen and Skou characterized probabilistic bisimilarity over reactive probabilistic systems with a logic including true, negation, conjunction, and a diamond modality decorated with a probabilistic lower bound. Later on, Desharnais,…
Within classical propositional logic, assigning probabilities to formulas is shown to be equivalent to assigning probabilities to valuations. A novel notion of probabilistic entailment enjoying desirable properties of logical consequence is…
This thesis is concerned with quantitative verification, that is, the verification of quantitative properties of quantitative systems. These systems are found in numerous applications, and their quantitative verification is important, but…
On the basis of the general character and operation of the process of perception, a formalism is sought to mathematically describe the subjective or abstract/mental process of perception. It is shown that the formalism of orthodox quantum…
The analysis of logarithmic return distributions defined over large time scales is crucial for understanding the long-term dynamics of asset price movements. For large time scales of the order of two trading years, the anticipated Gaussian…
The probabilistic (or quantitative) modal mu-calculus is a fixed-point logic de- signed for expressing properties of probabilistic labeled transition systems (PLTS). Two semantics have been studied for this logic, both assigning to every…
The one-variable fragment of any first-order logic may be considered as a modal logic, where the universal and existential quantifiers are replaced by a box and diamond modality, respectively. In several cases, axiomatizations of algebraic…
Various effects in human cognition, often considered `non-classical', have been argued to be most naturally modelled by quantum-like models of decision making. We extend this approach to describe models of cognition and decision-making in…
We study the process of observation (measurement), within the framework of a `perspectival' (`relational', `relative state') version of the modal interpretation of quantum mechanics. We show that if we assume certain features of…
Game comonads provide categorical semantics for comparison games in Finite Model Theory, thus providing an abstract characterisation of logical equivalence for a wide range of logics, each one captured through a specific choice of comonad.…
Recently, Baltag and van Benthem introduced a decidable logic of functional dependence (LFD) that extends the logic of Cylindrical Relativized Set Algebras (CRS) with atomic local dependence statements. Its semantics can be given in terms…