Related papers: Implicational Propositional Calculus: Tableaux and…
We develop a common semantic framework for the interpretation both of $\mathbf{IPC}$, the intuitionistic propositional calculus, and of logics weaker than $\mathbf{IPC}$ (substructural and subintuitionistic logics). This is done by proving…
A situation calculus is presented that provides a solution to the frame problem for hierarchical situations, that is, situations that have a modular structure in which parts of the situation behave in a relatively independent manner. This…
In this paper, we introduce a new method for calculating fractional integrals and differentials. The method involves an equation that we have obtained from infinite applied integration by parts. The equation works for special class of…
In this article, we deal with propositional calculi over a signature containing the classical implication $\to$ with the rules of modus ponens and substitution. For these calculi we consider few recognizing problems such as recognizing…
Following G. Mints(Kluwer 2000 and draft 2013), we present terminating and bicomplete proof searches in multi-succedent sequent calculi for intuitionistic propositional logic, fragments of intuitionistic predicate logic and full…
We study an extension of the Distributive Full Non-associative Lambek Calculus with iterative division operators. The iterative operators can be seen as representing iterative composition of linguistic resources or of actions. A complete…
This paper presents a novel SHOI tableau calculus which incorporates algebraic reasoning for deciding ontology consistency. Numerical restrictions imposed by nominals, existential and universal restrictions are encoded into a set of linear…
In this paper, we propose a new and simple approach to the approximation algorithms that are modified and improved from our published results. The computational and graphical examples are presented with the aid of Maple procedures.
We reformulate Pratt's tableau decision procedure of checking satisfiability of a set of formulas in PDL. Our formulation is simpler and more direct for implementation. Extending the method we give the first EXPTIME (optimal) tableau…
This is the first in a series of three papers on Algebraic Set Theory. Its main purpose is to lay the necessary groundwork for the next two parts, one on Realisability and the other on Sheaf Models in Algebraic Set Theory.
A major reason behind the success of probability calculus is that it possesses a number of valuable tools, which are based on the notion of probabilistic independence. In this paper, I identify a notion of logical independence that makes…
Compositionality is a key property for dealing with complexity, which has been studied from many points of view in diverse fields. Particularly, the composition of individual computations (or programs) has been widely studied almost since…
Imprecise probability is concerned with uncertainty about which probability distributions to use. It has applications in robust statistics and machine learning. We look at programming language models for imprecise probability. Our…
In the article we outline the set of Matlab functions that enable the computation of elliptic Integrals and Jacobian elliptic functions for real arguments. Correctness, robustness, efficiency and accuracy of the functions are discussed in…
We show that Propositional Dynamic Logic (PDL) has the Craig Interpolation Property. This question has been open for many years. Three proof attempts were published, but later criticized in the literature or retracted. Our proof is based on…
We propose a formalization of the three-tier causal hierarchy of association, intervention, and counterfactuals as a series of probabilistic logical languages. Our languages are of strictly increasing expressivity, the first capable of…
Modern saturation-based Automated Theorem Provers typically implement the superposition calculus for reasoning about first-order logic with or without equality. Practical implementations of this calculus use a variety of literal selections…
This paper obtains a completeness result for inequational reasoning with applicative terms without variables in a setting where the intended semantic models are the full structures, the full type hierarchies over preorders for the base…
We prove that all Set-based triposes are implicative triposes.
We seek random versions of some classical theorems on complex approximation by polynomials and rational functions, as well as investigate properties of random compact sets in connection to complex approximation.