Related papers: Nonclassical logics and multivariate truth values

We introduce proper display calculi for basic monotonic modal logic, the conditional logic CK and a number of their axiomatic extensions. These calculi are sound, complete, conservative and enjoy cut elimination and subformula property. Our…

This paper surveys main and recent studies on temporal logics in a broad sense by presenting various logic systems, dealing with various time structures, and discussing important features, such as decidability (or undecidability) results,…

Classical logic (the logic of non-constructive mathematics) is stronger than intuitionistic logic (the logic of constructive mathematics). Despite this, there are copies of classical logic in intuitionistic logic. All copies usually found…

A logic is defined that allows to express information about statistical probabilities and about degrees of belief in specific propositions. By interpreting the two types of probabilities in one common probability space, the semantics given…

We present a family of logics for reasoning about agents' positions and motion in the plane which have several potential applications in the area of multi-agent systems (MAS), such as multi-agent planning and robotics. The most general…

For a newcomer, paraconsistent logics can be difficult to grasp. Even experts in logic can find the concept of paraconsistency to be suspicious or misguided, if not actually wrong. The problem is that although they usually have much in…

Defeasible logics provide several linguistic features to support the expression of defeasible knowledge. There is also a wide variety of such logics, expressing different intuitions about defeasible reasoning. However, the logics can only…

The aim of this paper is to give an introduction to our axiomatic logical analysis of relativity theories.

The problem is posed of establishing a possible relationship between a new type of Multi-verse representation, G\"odel undecidability theorems and the logic of classical, quantum mechanics and quantum gravity. For this purpose example cases…

There is knowledge. There is belief. And there is tacit agreement.' 'We may talk about objects. We may talk about attributes of the objects. Or we may talk both about objects and their attributes.' This work inspects tacit agreements on…

Probability theory as extended logic is completed such that essentially any probability may be determined. This is done by considering propositional logic (as opposed to predicate logic) as syntactically suffcient and imposing a symmetry…

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…

This paper gives a generative model of the interpretation of formal logic for data-driven logical reasoning. The key idea is to represent the interpretation as likelihood of a formula being true given a model of formal logic. Using the…

Negation is both an operation in formal logic and in natural language by which a proposition is replaced by one stating the opposite, as by the addition of "not" or another negation cue. Treating negation in an adequate way is required for…

It has recently been discovered that both quantum and classical propositional logics can be modelled by classes of non-orthomodular and thus non-distributive lattices that properly contain standard orthomodular and Boolean classes,…

Weighted monadic second-order logic is a weighted extension of monadic second-order logic that captures exactly the behaviour of weighted automata. Its semantics is parameterized with respect to a semiring on which the values that weighted…

The notion of a real-valued function is central to mathematics, computer science, and many other scientific fields. Despite this importance, there are hardly any positive results on decision procedures for predicate logical theories that…

Defeasible logic is a rule-based nonmonotonic logic, with both strict and defeasible rules, and a priority relation on rules. We show that inference in the propositional form of the logic can be performed in linear time. This contrasts…

Although conventional logical systems based on logical calculi have been successfully used in mathematics and beyond, they have definite limitations that restrict their application in many cases. For instance, the principal condition for…

The standard notion of formal theory, in Logic, is in general biased exclusively towards assertion: it commonly refers only to collections of assertions that any agent who accepts the generating axioms of the theory should also be committed…