Related papers: Semantics of Computable Physical Models
We introduce operational semantics into games. And based on the operational semantics, we establish a full algebra of games, including basic algebra of games, algebra of concurrent games, recursion and abstraction. The algebra can be used…
Semantic composition remains an open problem for vector space models of semantics. In this paper, we explain how the probabilistic graphical model used in the framework of Functional Distributional Semantics can be interpreted as a…
Computability logic is a formal theory of computational tasks and resources. Its formulas represent interactive computational problems, logical operators stand for operations on computational problems, and validity of a formula is…
Approaching limitations of digital computing technologies have spurred research in neuromorphic and other unconventional approaches to computing. Here we argue that if we want to systematically engineer computing systems that are based on…
We offer a view of mathematics as an experimental science where axioms play the role of foundational theories like general relativity and quantum mechanics in physics. Under this view, axioms are provisional and inferred from experience…
This paper extends implication-space semantics to include first-order quantification. Implication-space semantics has recently been introduced as an inferentialist formal semantics that can capture nonmonotonic and nontransitive material…
A physical theory consists of the mathematical formalism and an interpretation, which contains the definition of symbols, measurement assignments, concepts and principles, and an ontology. We present a scheme to classify these different…
We propose a definition of quantum computable functions as mappings between superpositions of natural numbers to probability distributions of natural numbers. Each function is obtained as a limit of an infinite computation of a quantum…
Formal semantics offers a complete and rigorous definition of a language. It is important to define different semantic models for a language and different models serve different purposes. Building equivalence between different semantic…
Classification is an important goal in many branches of mathematics. The idea is to describe the members of some class of mathematical objects, up to isomorphism or other important equivalence in terms of relatively simple invariants. Where…
Currently it is widely accepted that the language of science is mathematics. This book explores an alternative idea where the future of science is based on the language of algorithms and programs. How such a language can actually be…
In this chapter, we explore how (Type-2) computable distributions can be used to give both (algorithmic) sampling and distributional semantics to probabilistic programs with continuous distributions. Towards this end, we sketch an encoding…
Despite its centrality in the philosophy of cognitive science, there has been little prior philosophical work engaging with the notion of representation in contemporary NLP practice. This paper attempts to fill that lacuna: drawing on ideas…
In this article, the notion of a mathematical model in science is attempted to be enlightened from several points of view. In particular, it is shown that mathematical models are introduced differently and used differently in different…
The paper relates two variants of semantic models for natural language, logical functional models and compositional distributional vector space models, by transferring the logic and reasoning from the logical to the distributional models.…
This article is a semitutorial-style survey of computability logic. An extended online version of it is maintained at http://www.csc.villanova.edu/~japaridz/CL/ .
We describe several views of the semantics of a simple programming language as formal documents in the calculus of inductive constructions that can be verified by the Coq proof system. Covered aspects are natural semantics, denotational…
We analyze the informal semantic conception of proof and axiomatize the proof relation and the provability operator. A self referential propositional calculus which admits provable liar type sentences is introduced and proven consistent. We…
The classical simulation of physical processes using standard models of computation is fraught with problems. On the other hand, attempts at modelling real-world computation with the aim of isolating its hypercomputational content have…
We propose FC, a new logic on words that combines finite model theory with the theory of concatenation - a first-order logic that is based on word equations. Like the theory of concatenation, FC is built around word equations; in contrast…