相关论文: Many concepts and two logics of algorithmic reduct…
Although many investigators affirm a desire to build reasoning systems that behave consistently with the axiomatic basis defined by probability theory and utility theory, limited resources for engineering and computation can make a complete…
While probability theory is normally applied to external environments, there has been some recent interest in probabilistic modeling of the outputs of computations that are too expensive to run. Since mathematical logic is a powerful tool…
This paper introduces a new notion of quantum recursion of which the control flow of the computation is quantum rather than classical as in the notions of recursion considered in the previous studies of quantum programming. A typical…
Despite significant achievements and current interest in machine learning and artificial intelligence, the quest for a theory of intelligence, allowing general and efficient problem solving, has done little progress. This work tries to…
Transformers have recently been shown to be capable of reliably performing logical reasoning over facts and rules expressed in natural language, but abductive reasoning - inference to the best explanation of an unexpected observation - has…
We introduce the notion of implicative algebra, a simple algebraic structure intended to factorize the model constructions underlying forcing and realizability (both in intuitionistic and classical logic). The salient feature of this…
This paper proposes a new approach to defining and expressing algorithms: the notion of {\it task logical} algorithms. This notion allows the user to define an algorithm for a task $T$ as a set of agents who can collectively perform $T$.…
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…
Many semantical aspects of programming languages, such as their operational semantics and their type assignment calculi, are specified by describing appropriate proof systems. Recent research has identified two proof-theoretic features that…
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…
This paper is an extended version of our work in \cite{Ca2025}. We extend the concept of effective reducibility between statements of set theory with ordinal Turing machines (OTMs) explored in \cite{Ca2018} for $\Pi_{2}$-statements to…
The goal of computational logic is to allow us to model computation as well as to reason about it. We argue that a computational logic must be able to model interactive computation. We show that first-order logic cannot model interactive…
We survey concepts at the frontier of research connecting artificial, animal and human cognition to computation and information processing---from the Turing test to Searle's Chinese Room argument, from Integrated Information Theory to…
We introduce an operational rewriting-based semantics for strictly positive nested higher-order (co)inductive types. The semantics takes into account the "limits" of infinite reduction sequences. This may be seen as a refinement and…
Type-free systems of logic are designed to consistently handle significant instances of self-reference. Some consistent type-free systems also have the feature of allowing the sort of general abstraction or comprehension principle that…
Abductive reasoning is a popular non-monotonic paradigm that aims to explain observed symptoms and manifestations. It has many applications, such as diagnosis and planning in artificial intelligence and database updates. In propositional…
Recursive analysis was introduced by A. Turing [1936], A. Grzegorczyk [1955], and D. Lacombe [1955]. It is based on a discrete mechanical framework that can be used to model computation over the real numbers. In this context the…
We investigate an unsuspected connection between logical connectives with non-harmonious deduction rules, such as Prior's tonk, and quantum computing. We argue that these connectives model the information-erasure, the non-reversibility, and…
This paper is a reflexion on the computability of natural language semantics. It does not contain a new model or new results in the formal semantics of natural language: it is rather a computational analysis of the logical models and…
This paper shows that, even at the most basic level, the parallel, countable branching and uncountable branching recurrences of Computability Logic (see http://www.cis.upenn.edu/~giorgi/cl.html) validate different principles.