Related papers: Tho Modal Logic of Minimal Upper Bounds

The first-order theory of MALL (multiplicative, additive linear logic) over only equalities is an interesting but weak logic since it cannot capture unbounded (infinite) behavior. Instead of accounting for unbounded behavior via the…

This paper from 2008 is the first in a series of three related papers on modal methods in interpretability logics and applications. In this first paper the foundations are laid for later results. These foundations consist of a thorough…

The aim of this paper is to propose a many-valued modal framework to formalize reasoning with both graded preferences and propositions, in the style of van Benthem et al.'s classical modal logics for preferences. To do so, we start from Bou…

This paper proposes an approach to information-based logics using many-logic modal structures (MLMS). These structures can express accessibility relations between worlds with different underlying logics by anchoring them to a base lattice,…

In probabilistic transition systems, behavioural metrics provide a more fine-grained and stable measure of system equivalence than crisp notions of bisimilarity. They correlate strongly to quantitative probabilistic logics, and in fact the…

Possibilistic logic has been proposed as a numerical formalism for reasoning with uncertainty. There has been interest in developing qualitative accounts of possibility, as well as an explanation of the relationship between possibility and…

Modal logics are widely used in computer science. The complexity of their satisfiability problems has been an active field of research since the 1970s. We prove that even very "simple" modal logics can be undecidable: We show that there is…

The fuzzy modality `probably` is interpreted over probabilistic type spaces by taking expected truth values. The arising probabilistic fuzzy description logic is invariant under probabilistic bisimilarity; more informatively, it is…

This paper introduces modal independence logic MIL, a modal logic that can explicitly talk about independence among propositional variables. Formulas of MIL are not evaluated in worlds but in sets of worlds, so called teams. In this vein,…

We show undecidability of the satisfiability problem of what is arguably the simplest non-sub-Boolean modal logic with an implicit notion of binding. This work enriches the series of existing results of undecidability of modal logics with…

We combine the concepts of modal logics and many-valued logics in a general and comprehensive way. Namely, given any finite linearly ordered set of truth values and any set of propositional connectives defined by truth tables, we define the…

We present a fuzzy (or quantitative) version of the van Benthem theorem, which characterizes propositional modal logic as the bisimulation-invariant fragment of first-order logic. Specifically, we consider a first-order fuzzy predicate…

We develop a denotational semantics of muLL, a version of propositional Linear Logic with least and greatest fixed points extending David Baelde's propositional muMALL with exponentials. Our general categorical setting is based on the…

We introduce an intuitionistic modal logic strictly contained in the intuitionistic modal logic IK and being an appropriate candidate for the title of ``minimal normal intuitionistic modal logic''.

A modal logic based on quantum logic is formalized in its simplest possible form. Specifically, a relational semantics and a sequent calculus are provided, and the soundness and the completeness theorems connecting both notions are…

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,…

We propose a new formalism for specifying and reasoning about problems that involve heterogeneous "pieces of information" -- large collections of data, decision procedures of any kind and complexity and connections between them. The essence…

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…

Originally developed as a theory of consciousness, integrated information theory provides a mathematical framework to quantify the causal irreducibility of systems and subsets of units in the system. Specifically, mechanism integrated…

The famous van Benthem theorem states that modal logic corresponds exactly to the fragment of first-order logic that is invariant under bisimulation. In this article we prove an exact analogue of this theorem in the framework of modal…