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3 Fundamenta Informaticae

3 2009

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Testing Semantics for RTPA

Llana L., Núnez M.

Fundamenta Informaticae

2009

Vol. 90, nr 3

305-335

The language RTPA, Real Time Process Algebra, has been created to enable rigorous treatment of knowledge representation and manipulation in terms of to be I to have / to do in a formal and coherent framework. This language has been designed to cope with the three dimensions involved in the problem of software specification: (i) mathematical operations, (ii) event/process timing, and (iii) memory manipulation. In this paper we focus on giving a testing semantics to the second dimension: Process timing dimension. First, we will provide a SOS like operational semantics for the process relations of RTPA. Next, we will define what a test is and we will introduce a relation based on which tests are passed by processes. Finally, we will obtain an operational characterization that can be used as a first step to define a denotational sematics sound and complete with respect the testing semantics.

Paradigms of Denotational Mathematics for Cognitive Informatics and Cognitive Computing

Wang Y.

Fundamenta Informaticae

2009

Vol. 90, nr 3

283-303

The abstract, rigorous, and expressive needs in cognitive informatics, intelligence science, software science, and knowledge science lead to new forms of mathematics collectively known as denotational mathematics. Denotational mathematics is a category of expressive mathematical structures that deals with high level mathematical entities beyond numbers and sets, such as abstract objects, complex relations, behavioral information, concepts, knowledge, processes, and systems. Denotational mathematics is usually in the form of abstract algebra that is a branch of mathematics in which a system of abstract notations is adopted to denote relations of abstract mathematical entities and their algebraic operations based on given axioms and laws. Four paradigms of denotational mathematics, known as concept algebra, system algebra, Real-Time Process Algebra (RTPA), and Visual Semantic Algebra (VSA), are introduced in this paper. Applications of denotational mathematics in cognitive informatics and computational intelligence are elaborated. Denotational mathematics is widely applicable to model and manipulate complex architectures and behaviors of both humans and intelligent systems, as well as long chains of inference processes.

A Formal Syntax of Natural Languages and the Deductive Grammar

Wang Y.

Fundamenta Informaticae

2009

Vol. 90, nr 4

353-368

This paper presents a formal syntax framework of natural languages for computational linguistics. The abstract syntax of natural languages, particularly English, and their formal manipulations are described. On the basis of the abstract syntax, a universal language processing model and the deductive grammar of English are developed toward the formalization of Chomsky's universal grammar in linguistics. Comparative analyses of natural and programming languages, as well as the linguistic perception on software engineering, are discussed. A wide range of applications of the deductive grammar of English have been explored in language acquisition, comprehension, generation, and processing in cognitive informatics, computational intelligence, and cognitive computing.