Related papers: Domain Theory for Modeling OOP: A Summary
Relational data model defines a specification of a type "relation". However, its simplicity does not mean that the system implementing this model must operate with structures having the same simplicity. We consider two principles allowing…
Out-of-distribution (OOD) generalization is a favorable yet challenging property for deep neural networks. The core challenges lie in the limited availability of source domains that help models learn an invariant representation from the…
This monograph is an ongoing revision of "Lectures On A Mathematical Theory of Computation" by Dana Scott. Scott's monograph uses a formulation of domains called neighborhood systems in which finite elements are selected subsets of a master…
The assumption of complete domain knowledge is not warranted for robot planning and decision-making in the real world. It could be due to design flaws or arise from domain ramifications or qualifications. In such cases, existing planning…
The paper tackles the issue of mapping logic axioms formalised in the Ontology Web Language (OWL) within the Object-Oriented Programming (OOP) paradigm. The issues of mapping OWL axioms hierarchies and OOP objects hierarchies are due to…
We introduce a taxonomy of objects for EO programming language. This taxonomy is designed with a few principles in mind: non-redundancy, simplicity, and so on. The taxonomy is supposed to be used as a navigation map by EO programmers. It…
This paper presents a new foundational approach to information theory based on the concept of the information efficiency of a recursive function, which is defined as the difference between the information in the input and the output. The…
Constraint logic programming combines declarativity and efficiency thanks to constraint solvers implemented for specific domains. Value withdrawal explanations have been efficiently used in several constraints programming environments but…
The paper describes a mechanism for indirect object representation and access (ORA) in programming languages. The mechanism is based on using a new programming construct which is referred to as concept. Concept consists of one object class…
Higher-order quantum theory is an extension of quantum theory where one introduces transformations whose input and output are transformations, thus generalizing the notion of channels and quantum operations. The generalization then goes…
We introduce a framework that represents a dynamic program as a family of operators acting on a partially ordered set. We provide an optimality theory based only on order-theoretic assumptions and show how applications across almost all…
Godel's theory T can be understood as a theory of the simply-typed lambda calculus that is extended to include the constant 0, the successor function S, and the operator R_tau for primitive recursion on objects of type tau. It is known that…
Neural ordinary differential equations (NODEs) is an invertible neural network architecture promising for its free-form Jacobian and the availability of a tractable Jacobian determinant estimator. Recently, the representation power of NODEs…
Formal Concept Analysis has proven to be an effective method of restructuring complete lattices and various algebraic domains. In this paper, the notions of attribute continuous formal context and continuous formal concept are introduced by…
While concepts and tools from Theoretical Computer Science are regularly applied to, and significantly support, software development for discrete problems, Numerical Engineering largely employs recipes and methods whose correctness and…
A classic result in formal language theory is the equivalence among non-counting, or aperiodic, regular languages, and languages defined through star-free regular expressions, or first-order logic. Past attempts to extend this result beyond…
We develop the theory of continuous and algebraic domains in constructive and predicative univalent foundations, building upon our earlier work on basic domain theory in this setting. That we work predicatively means that we do not assume…
The paper proposes a theoretical approach of the debugging of constraint programs based on a notion of explanation tree. The proposed approach is an attempt to adapt algorithmic debugging to constraint programming. In this theoretical…
The cost of large scale data collection and annotation often makes the application of machine learning algorithms to new tasks or datasets prohibitively expensive. One approach circumventing this cost is training models on synthetic data…
We describe a Martin-L\"of-style dependent type theory, called Cocon, that allows us to mix the intensional function space that is used to represent higher-order abstract syntax (HOAS) trees with the extensional function space that…