Related papers: Paraconsistentization and many-valued logics
We extend the simply-typed guarded $\lambda$-calculus with discrete probabilities and endow it with a program logic for reasoning about relational properties of guarded probabilistic computations. This provides a framework for programming…
Boolean grammars generalize context-free rewriting by extending the possibilities when dealing with different rules for the same nonterminal symbol. By allowing not only disjunction (as in the case of usual context-free grammars), but also…
While Large language models (LLMs) have proved able to address some complex reasoning tasks, we also know that they are highly sensitive to input variation, which can lead to different solution paths and final answers. Answer consistency…
Subtyping, also known as subtype polymorphism, is a concept extensively studied in programming language theory, delineating the substitutability relation among datatypes. This property ensures that programs designed for supertype objects…
Logical paradoxes and inconsistent information pose deep challenges in epistemology and the philosophy of logic. Classical systems typically handle contradictions only through external checks or by altering the logical framework, as in…
We calculate analytically the probabilities for intuitive and counterintuitive transitions in a three-state system, in which two parallel energies are crossed by a third, tilted energy. The state with the tilted energy is coupled to the…
Linear-time computational techniques have been developed for combining evidence which is available on a number of contending hypotheses. They offer a means of making the computation-intensive calculations involved more efficient in certain…
In this paper, we investigate superintegrable systems which separate in parabolic coordinates and admit a third-order integral of motion. We give the corresponding determining equations and show that all such systems are multi-separable and…
Linear implication can represent state transitions, but real transition systems operate under temporal, stochastic or probabilistic constraints that are not directly representable in ordinary linear logic. We propose a general modal…
This paper focuses on the mathematical approaches to the analysis of stability that is a crucial step in the design of dynamical systems. Three methods are presented, namely, absolutely integrable impulse response, Fourier integral, and…
We introduce a framework that allows for the construction of sequent systems for expressive description logics extending ALC. Our framework not only covers a wide array of common description logics, but also allows for sequent systems to be…
We present a class of systems for which the signal-to-noise ratio as a function of the noise level may display a multiplicity of maxima. This phenomenon, referred to as stochastic multiresonance, indicates the possibility that periodic…
We introduce the notion of a {\it mock tridiagonal system}. This is a generalization of a tridiagonal system in which the irreducibility assumption is replaced by a certain non-vanishing condition. We show how mock tridiagonal systems can…
In this paper we study possibilities of using hierarchical reasoning, symbol elimination and model generation for the verification of parametric systems, where the parameters can be constants or functions. Our goal is to automatically…
In this article the algorithm for transformation of logic functions which are given by truth tables is considered. The suggested algorithm allows the transformation of many-valued logic functions with the required number of variables and…
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…
Binary logic and devices have been in used since inception with advancement and technology and millennium gate design era. The development in binary logic has become tedious and cumbersome. Multivalued logic enables significant more…
Given a consequence relation in many-valued logic, what connectives can be defined? For instance, does there always exist a conditional operator internalizing the consequence relation, and which form should it take? In this paper, we pose…
In this short paper, we are concerned with the blowup phenomenon of stochastic parabolic equations. By using comparison principle and the results of deterministic parabolic equations, we obtain blowup results of solutions for stochastic…
We present a procedure for the construction of multi-valued t-norms and t-conorms. Our procedure makes use of a pair of single-valued t-norms and the respective dual t-conorms and produces interval-valued t-norms and t-conorms. In this…