Related papers: Syntax-semantics interface: an algebraic model
As first main contribution, this thesis characterises the PROP SVk of linear subspaces over a field k - an important domain of interpretation for circuit diagrams appearing in diverse research areas. We present by generators and equations…
Rule-based reasoning is an essential part of human intelligence prominently formalized in artificial intelligence research via logic programs. Describing complex objects as the composition of elementary ones is a common strategy in computer…
The paper provides a survey of semantic methods for solution of fundamental tasks in mathematical knowledge management. Ontological models and formalisms are discussed. We propose an ontology of mathematical knowledge, covering a wide range…
We give an algebraic characterization of the syntax and semantics of a class of simply-typed languages, such as the language PCF: we characterize simply-typed binding syntax equipped with reduction rules via a universal property, namely as…
Tarski gave a general semantics for deductive reasoning: a formula a may be deduced from a set A of formulas iff a holds in all models in which each of the elements of A holds. A more liberal semantics has been considered: a formula a may…
Methods developed for the analysis of non-linear integrable models are used in the harmonic superspace (HS) framework. These methods, when applied to the HS, can lead to extract more information about the meaning of integrability in…
Convolution is a ubiquitous operation in mathematics and computing. The Kripke semantics for substructural and interval logics motivates its study for quantale-valued functions relative to ternary relations. The resulting notion of…
This article is an exploratory account of the the non-monotonic behaviour of conceptual associations in the light of context. Computational approximations of conceptual space are furnished by semantic space models which are emerging from…
We investigate to what extent renormalization can be understood as an algebraic manipulation on concatenated one-loop integrals. We find that the resulting algebra indicates a useful connection to knot theory.
Due to the increased complexity of software development projects more and more systems are described by models. The sheer size makes it impractical to describe these systems by a single model. Instead many models are developed that provide…
In the quest to give a formal compositional semantics to natural languages, semanticists have started turning their attention to phenomena that have been also considered as parts of pragmatics (e.g., discourse anaphora and presupposition…
We describe a formal model for annotating linguistic artifacts, from which we derive an application programming interface (API) to a suite of tools for manipulating these annotations. The abstract logical model provides for a range of…
Probabilistic context-free grammars have a long-term record of use as generative models in machine learning and symbolic regression. When used for symbolic regression, they generate algebraic expressions. We define the latter as equivalence…
Abstraction is a powerful idea widely used in science, to model, reason and explain the behavior of systems in a more tractable search space, by omitting irrelevant details. While notions of abstraction have matured for deterministic…
Abstraction is a key verification technique to improve scalability. However, its use for neural networks is so far extremely limited. Previous approaches for abstracting classification networks replace several neurons with one of them that…
Symmetry plays a central role in accelerating symbolic computation involving polynomials. This chapter surveys recent developments and foundational methods that leverage the inherent symmetries of polynomial systems to reduce complexity,…
Natural language syntax can serve as a major test for how to integrate two infamously distinct frameworks: symbolic representations and connectionist neural networks. Building on a recent neurocomputational architecture for syntax (ROSE), I…
Semantic communication has emerged as a promising paradigm to address the challenges of next-generation communication networks. While some progress has been made in its conceptualization, fundamental questions remain unresolved. In this…
Combining abstract, symbolic reasoning with continuous neural reasoning is a grand challenge of representation learning. As a step in this direction, we propose a new architecture, called neural equivalence networks, for the problem of…
In this introductory article we present the basics of an approach to implementing computational interpreting of natural language aiming to model the meanings of words and phrases. Unlike other approaches, we attempt to define the meanings…