Related papers: Relevant First-Order Logic $LP^\#$ and Curry's Par…

This paper presents and discusses several methods for reasoning from inconsistent knowledge bases. A so-called argumentative-consequence relation taking into account the existence of consistent arguments in favor of a conclusion and the…

This paper proposes the meeting of fuzzy logic with paraconsistency in a very precise and foundational way. Specifically, in this paper we introduce expansions of the fuzzy logic MTL by means of primitive operators for consistency and…

The investigations on higher-order type theories and on the related notion of parametric polymorphism constitute the technical counterpart of the old foundational problem of the circularity (or impredicativity) of second and higher order…

In 1952 P. F. Strawson proposed a logic of presuppositions. It is an interpretation of Aristotelian logic, i.e. of the logic of the traditional syllogism. In 1981 Richard Diaz published a monograph in which he presented truth-relevant…

We study a nonlinear stochastic partial differential equation whose solution is the conditional log-Laplace functional of a superprocess in a random environment. We establish its existence and uniqueness by smoothing out the nonlinear term…

We propose a novel logic, called Frame Logic (FL), that extends first-order logic (with recursive definitions) using a construct Sp(.) that captures the implicit supports of formulas -- the precise subset of the universe upon which their…

For many standard models of random structure, first-order logic sentences exhibit a convergence phenomenon on random inputs. The most well-known example is for random graphs with constant edge probability, where the probabilities of…

The logic of constant domains is intuitionistic logic extended with the so-called forall-shift axiom, a classically valid statement which implies the excluded middle over decidable formulas. Surprisingly, this logic is constructive and so…

We augment LP with a strong conditional operator, to yield a logic we call "strong LP," or LP=>. The resulting logic can speak of consistency in more discriminating ways, but introduces new possibilities for trivializing paradoxes.

Several approaches to the formulation of a fractional theory of calculus of "variable order" have appeared in the literature over the years. Unfortunately, most of these proposals lack a rigorous mathematical framework. We consider an…

Contextuality and nonlocality are two fundamental properties of nature. Hardy's proof is considered the simplest proof of nonlocality and can also be seen as a particular violation of the simplest Bell inequality. A fundamental question is:…

How can non-classical logic contribute to the analysis of complexity in computer science? In this paper, we give a step towards this question, taking a logical model-theoretic approach to the analysis of complexity in fuzzy constraint…

In this paper the 3-valued paraconsistent first-order logic QCiore is studied from the point of view of Model Theory. The semantics for QCiore is given by partial structures, which are first-order structures in which each n-ary predicate R…

In this note we study the effect of adding fixed points to justification logics. We introduce two extensions of justification logics: extensions by fixed point (or diagonal) operators, and extensions by least fixed points. The former is a…

Strategy Logic (SL, for short) has been introduced by Mogavero, Murano, and Vardi as a useful formalism for reasoning explicitly about strategies, as first-order objects, in multi-agent concurrent games. This logic turns out to be very…

This paper concerns the paraconsistent logic LPQ$^{\supset,\mathsf{F}}$ and an application of it in the area of relational database theory. The notions of a relational database, a query applicable to a relational database, and a consistent…

This paper presents PFLP, a library for probabilistic programming in the functional logic programming language Curry. It demonstrates how the concepts of a functional logic programming language support the implementation of a library for…

I'll discuss how Goedel's paradox "This statement is false/unprovable" yields his famous result on the limits of axiomatic reasoning. I'll contrast that with my work, which is based on the paradox of "The first uninteresting positive whole…

Logical formalisms provide a natural and concise means for specifying and reasoning about preferences. In this paper, we propose lexicographic logic, an extension of classical propositional logic that can express a variety of preferences,…

First-Order Logic (FOL) is widely regarded as one of the most important foundations for knowledge representation. Nevertheless, in this paper, we argue that FOL has several critical issues for this purpose. Instead, we propose an…