Related papers: Fundamentals of computability logic 2020
This paper constructs a cirquent calculus system and proves its soundness and completeness with respect to the semantics of computability logic (see http://www.cis.upenn.edu/~giorgi/cl.html). The logical vocabulary of the system consists of…
This article reformulates the theory of computable physical models, previously introduced by the author, as a branch of applied model theory in first-order logic. It provides a semantic approach to the philosophy of science that…
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…
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…
This paper surveys main and recent studies on temporal logics in a broad sense by presenting various logic systems, dealing with various time structures, and discussing important features, such as decidability (or undecidability) results,…
As suggested by the title, this paper is a survey of recent results and questions on the collection of computably enumerable sets under inclusion. This is not a broad survey but one focused on the author's and a few others' current…
This paper from 2000 is a presentation of a status qu{\ae}stionis at that tiime, to wit of the problem of the interpretability logic of {\em all}\/ reasonable arithmetical theories. We present both the arithmetical side and the modal side…
We present an extension to the $\mathtt{mathlib}$ library of the Lean theorem prover formalizing the foundations of computability theory. We use primitive recursive functions and partial recursive functions as the main objects of study, and…
We present a logical framework that enables us to define a formal theory of computational trust in which this notion is analysed in terms of epistemic attitudes towards the possible objects of trust and in relation to existing evidence in…
Computability logic (CoL) (see http://www.cis.upenn.edu/~giorgi/cl.html) is a recently introduced semantical platform and ambitious program for redeveloping logic as a formal theory of computability, as opposed to the formal theory of truth…
This volume contains a selection of papers presented at Linearity&TLLA 2020, namely the Second Joint International Workshop on Linearity & Trends in Linear Logic and Applications, held on June 29-30, 2020 online. (The workshop was supposed…
Philosophy of science attempts to describe all parts of the scientific process in a general way in order to facilitate the description, execution and improvements of this process. So far, all proposed philosophies have only covered existing…
The blog is somewhat shorter than in previous years, It contains new insights in a variety of areas, including computability, quantum algorithmic version of the SMB theorem, descriptions of groups (both discrete and profinite), metric…
The earlier paper "Introduction to clarithmetic I" constructed an axiomatic system of arithmetic based on computability logic (see http://www.cis.upenn.edu/~giorgi/cl.html), and proved its soundness and extensional completeness with respect…
In this article we determine the implicational fragments of most of the known subintuitionistic logics.
This paper introduces a new simplified version of the countable branching recurrence of Computability Logic, proves its equivalence to the old one, and shows that the basic logic induced by it is a proper superset of the basic logic induced…
The blog has several entries on group theory interacting with computability and wider logic, several open questions, and an entry on undecidability in physics.
These lecture notes are an informal introduction to the theory of computational complexity and its links to quantum computing and statistical mechanics.
The importance of transformations and normal forms in logic programming, and generally in computer science, is well documented. This paper investigates transformations and normal forms in the context of Defeasible Logic, a simple but…
In the practical deployment of machine learning (ML) models, missing data represents a recurring challenge. Missing data is often addressed when training ML models. But missing data also needs to be addressed when deciding predictions and…