相关论文: Paraconsistency of Interactive Computation

Classical logic predicts that everything (thus nothing useful at all) follows from inconsistency. A paraconsistent logic is a logic where an inconsistency does not lead to such an explosion, and since in practice consistency is difficult to…

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…

In the same sense as classical logic is a formal theory of truth, the recently initiated approach called computability logic is a formal theory of computability. It understands (interactive) computational problems as games played by a…

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…

We apply a paraconsistent logic to reason about fractions.

The recently initiated approach called computability logic is a formal theory of interactive computation. See a comprehensive online source on the subject at http://www.cis.upenn.edu/~giorgi/cl.html . The present paper contains a soundness…

Excellent computer simulations are done for a purpose. The most valid purposes are to explore uncharted territory, to resolve a well-posed scientific or technical question, or to make a design choice. Stand-alone modeling can serve the…

We describe a method to axiomatize computations in deterministic Turing machines. When applied to computations in non-deterministic Turing machines, this method may produce contradictory (and therefore trivial) theories, considering…

Computability logic is a formal theory of (interactive) computability in the same sense as classical logic is a formal theory of truth. This approach was initiated very recently in "Introduction to computability logic" (Annals of Pure and…

Transparency is an essential requirement of machine learning based decision making systems that are deployed in real world. Often, transparency of a given system is achieved by providing explanations of the behavior and predictions of the…

Transparency is a fundamental requirement for decision making systems when these should be deployed in the real world. It is usually achieved by providing explanations of the system's behavior. A prominent and intuitive type of explanations…

Recent work shows issues of consistency with explanations, with methods generating local explanations that seem reasonable instance-wise, but that are inconsistent across instances. This suggests not only that instance-wise explanations can…

Language models now provide an interface to express and often solve general problems in natural language, yet their ultimate computational capabilities remain a major topic of scientific debate. Unlike a formal computer, a language model is…

We consider the issue of computability at the most fundamental level of physical reality: the Planck scale. To this aim, we consider the theoretical model of a quantum computer on a non commutative space background, which is a computational…

Data consistency is very desirable because strong semantic properties make it easier to write correct programs that perform as users expect. However, there are good reasons why consistency may have to be weakened to achieve other business…

Computability logic (CL) (see http://www.cis.upenn.edu/~giorgi/cl.html ) is a research program for redeveloping logic as a formal theory of computability, as opposed to the formal theory of truth which it has more traditionally been.…

Computability logic is a formal theory of computational tasks and resources. Formulas in it represent interactive computational problems, and "truth" is understood as algorithmic solvability. Interactive computational problems, in turn, are…

This paper presents a soundness and completeness proof for propositional intuitionistic calculus with respect to the semantics of computability logic. The latter interprets formulas as interactive computational problems, formalized as games…

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…

The paper gives a soundness and completeness proof for the implicative fragment of intuitionistic calculus with respect to the semantics of computability logic, which understands intuitionistic implication as interactive algorithmic…