Related papers: Disjunctive Probabilistic Modal Logic is Enough fo…
We present a propositional logic with fundamental probabilistic semantics, in which each formula is given a real measure in the interval $[0,1]$ that represents its degree of truth. This semantics replaces the binarity of classical logic,…
Behavioural equivalences can be characterized via bisimulations, modal logics and spoiler-defender games. In this paper we review these three perspectives in a coalgebraic setting, which allows us to generalize from the particular branching…
Modal probabilistic logics provide a framework for reasoning about probability in modal contexts, involving notions such as knowledge, belief, time, and action. In this paper, we study a particular family of these logics, extending the…
In the article we investigate three classes of extended Boolean Connexive Logics. Two of them are extensions of Modal and non-Modal Boolean Connexive Logics with a property of closure under an arbitrary number of negations. The remaining…
We introduce and develop a set-based semantics for asynchronous TeamLTL. We consider two canonical logics in this setting: the extensions of TeamLTL by the Boolean disjunction and by the Boolean negation. We establish fascinating…
In the context of natural deduction for propositional classical logic, with classicality given by the inference rule reductio ad absurdum, we investigate the De Morgan translation of disjunction in terms of negation and conjunction. Once…
We study fragments of first-order logic and of least fixed point logic that allow only unary negation: negation of formulas with at most one free variable. These logics generalize many interesting known formalisms, including modal logic and…
It is standard to regard the intuitionistic restriction of a classical logic as increasing the expressivity of the logic because the classical logic can be adequately represented in the intuitionistic logic by double-negation, while the…
Mechanisms for the automation of uncertainty are required for expert systems. Sometimes these mechanisms need to obey the properties of probabilistic reasoning. A purely numeric mechanism, like those proposed so far, cannot provide a…
In physics we often use very simple models to describe systems with many degrees of freedom, but it is not clear why or how this success can be transferred to the more complex biological context. We consider models for the joint…
This paper studies nested sequents for quantified modal logics. In particular, it considers extensions of the propositional modal logics definable by the axioms D, T, B, 4, and 5 with varying, increasing, decreasing, and constant domains.…
The dual or game-theoretical negation $\lnot$ of independence-friendly logic (IF) and dependence logic (D) exhibits an extreme degree of semantic indeterminacy in that for any pair of sentences $\phi$ and $\psi$ of IF/D, if $\phi$ and…
We study the relation between additivity and deduction theorems in the algebraic semantics of congruential modal logic. Additivity of the modal operator is well-known to imply the local deduction-detachment theorem. Our main theme is that…
The so-called paradoxes of material implication have motivated the development of many non-classical logics over the years \cite{aA75,nB77,aA89,gP89,sH96}. In this note, we investigate some of these paradoxes and classify them, over minimal…
We present a spectrum of trace-based, testing, and bisimulation equivalences for nondeterministic and probabilistic processes whose activities are all observable. For every equivalence under study, we examine the discriminating power of…
In an impressive series of papers, Krivine showed at the edge of the last decade how classical realizability provides a surprising technique to build models for classical theories. In particular, he proved that classical realizability…
Intuitionistic grammar logics fuse constructive and multi-modal reasoning while permitting the use of converse modalities, serving as a generalization of standard intuitionistic modal logics. In this paper, we provide definitions of these…
In order to enrich dynamic semantic theories with a `pragmatic' capacity, we combine dynamic and nonmonotonic (preferential) logics in a modal logic setting. We extend a fragment of Van Benthem and De Rijke's dynamic modal logic with…
This article presents modal versions of resource-conscious logics. We concentrate on extensions of variants of Linear Logic with one minimal non-normal modality. In earlier work, where we investigated agency in multi-agent systems, we have…
Attempts to replicate probabilistic reasoning in expert systems have typically overlooked a critical ingredient of that process. Probabilistic analysis typically requires extensive judgments regarding interdependencies among hypotheses and…