Related papers: Towards a Higher-Order Bialgebraic Denotational Se…
The complexity of modern software systems entails the need for reconfiguration mechanisms gov- erning the dynamic evolution of their execution configurations in response to both external stimulus or internal performance measures. Formally,…
Semantic text similarity plays an important role in software engineering tasks in which engineers are requested to clarify the semantics of descriptive labels (e.g., business terms, table column names) that are often consists of too short…
The recently proposed CP language adopts Compositional Programming: a new modular programming style that solves challenging problems such as the Expression Problem. CP is implemented on top of a polymorphic core language with disjoint…
Diassociative algebras form a categoy of algebras recently introduced by Loday. A diassociative algebra is a vector space endowed with two associative binary operations satisfying some very natural relations. Any diassociative algebra is an…
Substructural logics are formal logical systems that omit familiar structural rules of classical and intuitionistic logic such as contraction, weakening, exchange (commutativity), and associativity. This leads to a resource-sensitive…
Programs with a continuous state space or that interact with physical processes often require notions of equivalence going beyond the standard binary setting in which equivalence either holds or does not hold. In this paper we explore the…
Declarative modeling uses symbolic expressions to represent models. With such expressions one can formalize high-level mathematical computations on models that would be difficult or impossible to perform directly on a lower-level simulation…
In this paper, we propose a new operation, Generalised Sequential Crossover (GSCO) of words, which in some sense an abstract model of crossing over of the chromosomes in the living organisms. We extend GSCO over language $L$ iteratively…
Human cognition excels at symbolic reasoning, deducing abstract rules from limited samples. This has been explained using symbolic and connectionist approaches, inspiring the development of a neuro-symbolic architecture that combines both…
The mathematical framework of Stone duality is used to synthesize a number of hitherto separate developments in Theoretical Computer Science: - Domain Theory, the mathematical theory of computation introduced by Scott as a foundation for…
Deep learning is currently the subject of intensive study. However, fundamental concepts such as representations are not formally defined -- researchers "know them when they see them" -- and there is no common language for describing and…
In this thesis we use quasiorders on words to offer a new perspective on two well-studied problems from Formal Language Theory: deciding language inclusion and manipulating the finite automata representations of regular languages. First, we…
Deductive verification techniques for C11 programs have advanced significantly in recent years with the development of operational semantics and associated logics for increasingly large fragments of C11. However, these semantics and logics…
In this paper we introduced an algebraic semantics for process algebra in form of abstract data types. For that purpose, we developed a particular type of algebra, the seed algebra, which describes exactly the behavior of a process within a…
The idea of using unfolding as a way of computing a program semantics has been applied successfully to logic programs and has shown itself a powerful tool that provides concrete, implementable results, as its outcome is actually source…
We introduce a new setting, the category of $\omega$PAP spaces, for reasoning denotationally about expressive differentiable and probabilistic programming languages. Our semantics is general enough to assign meanings to most practical…
We define a novel, extensional, three-valued semantics for higher-order logic programs with negation. The new semantics is based on interpreting the types of the source language as three-valued Fitting-monotonic functions at all levels of…
In this paper, we show that theory of processes can be reduced to the theory of spatial logic. Firstly, we propose a spatial logic SL for higher order pi-calculus, and give an inference system of SL. The soundness and incompleteness of SL…
Recently an extension to higher-order logic -- called DHOL -- was introduced, enriching the language with dependent types, and creating a powerful extensional type theory. In this paper we propose two ways how choice can be added to DHOL.…
The purpose of this work is to complete the algebraic foundations of second-order languages from the viewpoint of categorical algebra as developed by Lawvere. To this end, this paper introduces the notion of second-order algebraic theory…