Related papers: Sense, reference, and computation
Mathematical Theory of Evidence (MTE) is known as a foundation for reasoning when knowledge is expressed at various levels of detail. Though much research effort has been committed to this theory since its foundation, many questions remain…
We propose a novel framework seamlessly providing key properties of both neural nets (learning) and symbolic logic (knowledge and reasoning). Every neuron has a meaning as a component of a formula in a weighted real-valued logic, yielding a…
We examine the convergence properties of sequences of nonnegative real numbers that satisfy a particular class of recursive inequalities, from the perspective of proof theory and computability theory. We first establish a number of results…
This paper presents evidence for the idea that much of artificial intelligence, human perception and cognition, mainstream computing, and mathematics, may be understood as compression of information via the matching and unification of…
The TTE approach to Computable Analysis is the study of so-called representations (encodings for continuous objects such as reals, functions, and sets) with respect to the notions of computability they induce. A rich variety of such…
The literature on concurrency theory offers a wealth of examples of characteristic-formula constructions for various behavioural relations over finite labelled transition systems and Kripke structures that are defined in terms of fixed…
This work describes the principled design of a theoretical framework leading to fast and accurate algorithmic information measures on finite multisets of finite strings by means of compression. One distinctive feature of our approach is to…
In the theory of answer set programming, two groups of rules are called strongly equivalent if, informally speaking, they have the same meaning in any context. The relationship between strong equivalence and the propositional logic of…
We investigate the computational properties of basic mathematical notions pertaining to $\mathbb{R}\rightarrow \mathbb{R}$-functions and subsets of $\mathbb{R}$, like finiteness, countability, (absolute) continuity, bounded variation,…
Inspired by empirical work in neuroscience for Bayesian approaches to brain function, we give a unified probabilistic account of various types of symbolic reasoning from data. We characterise them in terms of formal logic using the…
In musical compositions that include vocals, lyrics significantly contribute to artistic expression. Consequently, previous studies have introduced the concept of a recommendation system that suggests lyrics similar to a user's favorites or…
Truth refers to the satisfaction relation used to define the semantics of model-theoretic languages. The satisfaction relation for first order languages (truth classification), and the preservation of truth by first order interpretations…
Lawvere observed in his celebrated work on hyperdoctrines that the set-theoretic schema of comprehension can be elegantly expressed in the functorial language of categorical logic, as a comprehension structure on the functor…
This work is the first exploration of proof-theoretic semantics for a substructural logic. It focuses on the base-extension semantics (B-eS) for intuitionistic multiplicative linear logic (IMLL). The starting point is a review of…
In this paper, an application of automated theorem proving techniques to computational semantics is considered. In order to compute the presuppositions of a natural language discourse, several inference tasks arise. Instead of treating…
An important question concerning contextualized word embedding (CWE) models like BERT is how well they can represent different word senses, especially those in the long tail of uncommon senses. Rather than build a WSD system as in previous…
The categorical compositional distributional model of Coecke, Sadrzadeh and Clark provides a linguistically motivated procedure for computing the meaning of a sentence as a function of the distributional meaning of the words therein. The…
In his proof of Fermat's Last Theorem, Wiles deployed a commutative algebra technique, namely a numerical criterion for detecting isomorphisms of rings. In our recent work we pick up on Wiles' work and generalize the numerical criterion to…
Following the principles of Cognitive Grammar, we concentrate on a model for reference resolution that attempts to overcome the difficulties previous approaches, based on the fundamental assumption that all reference (independent on the…
We introduce a logical approach to formalizing statistical properties of machine learning. Specifically, we propose a formal model for statistical classification based on a Kripke model, and formalize various notions of classification…