Related papers: Note on paraconsistency and reasoning about fracti…
Real-valued logics underlie an increasing number of neuro-symbolic approaches, though typically their logical inference capabilities are characterized only qualitatively. We provide foundations for establishing the correctness and power of…
We consider a language together with the subword relation, the cover relation, and regular predicates. For such structures, we consider the extension of first-order logic by threshold- and modulo-counting quantifiers. Depending on the…
Recently, we have proposed a new diffusive representation for fractional derivatives and, based on this representation, suggested an algorithm for their numerical computation. From the construction of the algorithm, it is immediately…
We describe the theory of "flag paraproducts" and their relationship with the field of differential equations.
Argumentation is a non-monotonic process. This reflects the fact that argumentation involves uncertain information, and so new information can cause a change in the conclusions drawn. However, the base logic does not need to be…
Definitions and notations with historical references are given for some numerical coefficients commonly used to quantify relations among collections of objects for the purpose of expressing approximate knowledge and probabilistic reasoning.
We present two deductively equivalent calculi for non-deterministic many-valued logics. One is defined by axioms and the other - by rules of inference. The two calculi are obtained from the truth tables of the logic under consideration in a…
In this note we study some sequences whose ratio converges to the square root of rationals. Further we analyze some related sequences obtained when the above mentioned ratio simplifies.
We develop foundational aspects of stability theory in affine logic. On the one hand, we prove appropriate affine versions of many classical results, including definability of types, existence of non-forking extensions, and other…
We discuss a non-intuitive situation concerning percentages.
Counting propositional logic was recently introduced in relation to randomized computation and shown able to logically characterize the full counting hierarchy. In this paper we aim to clarify the intuitive meaning and expressive power of…
There have been a number of developments in measuring inconsistency in logic-based representations of knowledge. In contrast, the development of inconsistency measures for computational models of argument has been limited. To address this…
Cirquent calculus is a proof system with inherent ability to account for sharing subcomponents in logical expressions. Within its framework, this article constructs an axiomatization CL18 of the basic propositional fragment of computability…
In this paper paraconsistent second order arithmetic Z#2 with unrestricted comprehension scheme is proposed. We outline the development of certain portions of paraconsistent mathematics within paraconsistent second order arithmetic Z#2.In…
Consistency properties of concurrent computations, e.g., sequential consistency, linearizability, or eventual consistency, are essential for devising correct concurrent algorithms. In this paper, we present a logical formalization of such…
Analytical expressions are derived for the number of fractions with equal numerators in the Farey sequence of order $n$, $F_n$, and in the truncated Farey sequence $F_n^{1/k}$ containing all Farey fractions below $1/k$, with $1\leq k \leq…
Signed systems were introduced as a general, syntax-independent framework for paraconsistent reasoning, that is, non-trivialised reasoning from inconsistent information. In this paper, we show how the family of corresponding paraconsistent…
Predicting the future is an important component of decision making. In most situations, however, there is not enough information to make accurate predictions. In this paper, we develop a theory of causal reasoning for predictive inference…
Programming with logic for sophisticated applications must deal with recursion and negation, which together have created significant challenges in logic, leading to many different, conflicting semantics of rules. This paper describes a…
We introduce a logic specifically designed to support reasoning about social choice functions. The logic includes operators to capture strategic ability, and operators to capture agent preferences. We establish a correspondence between…