Formal languages

Object-Z is an object-oriented specification language which extends the Z language with classes, objects, inheritance and polymorphism that can be used to represent the specification of a complex system as collections of objects. There are a number of existing works that mapped Object-Z to C++ and Java programming languages. Since Python and Object-Z share many similarities, both are object-oriented paradigm, support set theory and predicate calculus moreover, Python is a functional programming language which is naturally closer to formal specifications, we propose a mapping from Object-Z specifications to Python code that covers some Object-Z constructs and express its specifications in Python to validate these specifications. The validations are used in the mapping covered preconditions, post-conditions, and invariants that are built using lambda function and Python's decorator. This work has found Python is an excellent language for developing libraries to map Object-Z specif...

In this paper we deal with the problem of estimating the marking of a labeled Petri net system based on the observation of transitions labels. In particular, we assume that a certain number of transitions are labeled with the empty string ε, while a different label taken from a given alphabet is assigned to all the other transitions. Transitions labeled with the empty string are called silent because their firing cannot be observed. Under some technical assumptions on the structure of the Tε -induced subnet, where Tε denotes the set of silent transitions, we formally prove that the set of markings consistent with the observed word can be represented by a linear system with a fixed structure that does not depend on the length of the observed word.

Formal methods have yet to achieve wide industrial acceptance for several reasons. They are not well integrated into established industrial software processes, their application requires significant abstraction and mathematical skills, and existing tools do not satisfactorily support the entire formal software development process. We have proposed a language called SOFL (Structured-Object-based-formal Language) and a SOFL methodology for system development that attempts to address these problems using an ...

An introductory summary of some aspects of formal language theory intended for an audience doing AGL experiments but without training on the formal side of things.
Presented at the workshop 'Formal Grammars, Informally'. Reading, December, 2017.

In graduate school, it became too cumbersome for me to look-up equations, theorems, proofs, and problem solutions from previous courses. I had three boxes full of notes and was going on my fourth. Due to the need to reference my notes periodically, the notes became more unorganized over time. That's when I decided to typeset them. I have been doing this for over a decade. Later in life, some colleagues asked if I could make these notes available to others (they were talking about themselves). I did. These notes can be downloaded for \it free \rm from the web site http://www.repec.org/ and can be found in the Library of Congress. Note that the beginning of each chapter lists the professor's name and affiliation. Additionally, the course number, the date the course was taken, and the text book are given. The reader may also notice that I have made more use of the page space than in the previous editions of this manuscript. Hence, the book is shorter. If this causes the reader problems, then simply copy the proofs onto a blank sheet of paper --- one line per algebraic manipulation. In this text, I put several algebraic manipulations on one line to save space. I thank Winston for helping typeset the notes.

Beyond its widespread use for representing technical aspects and matters of building and construction science, Building information modeling (BIM) can be used to represent architectural relationships and rules drawn from aesthetic theory. This research suggests that BIM provides not only vocabulary but also syntactical tools that can be used to capture an architectural language. In a case study using Richard Meier's language for single-family detached houses, a BIM template has been devised to represent the aesthetic concepts and relations therein. The template employs parameterized conceptual mass objects, syntactical rules, and a library of architectonic elements, such as walls, roofs, columns, windows, doors, and railings. It constrains any design produced using the template to a grammatically consistent expression or style. The template has been used as the starting point for modeling the Smith House, the Douglas House, and others created by the authors, demonstrating that the aesthetic template is general to many variations. Designing with the template to produce a unique but conforming design further illustrates the generality and expressiveness of the language. Having made the formal language explicit, in terms of syntactical rules and vocabulary, it becomes easier to vary the formal grammar and concrete vocabulary to produce variant languages and styles. Accordingly, this approach is not limited to a specific style, such as Richard Meier's. Future research can be conducted to demonstrate how designing with BIM can support stylistic change. Adoption of this approach in practice could improve the consistency of architectural designs and their coherence to defined styles, potentially increasing the general level of aesthetic expression in our built environment.

10th International Conference on Foundations of Computer Science & Technology (FCST 2022) will act as a major forum for the presentation of innovative ideas, approaches, developments, and research projects in the areas of Foundations of Computer Science & Technology. It will also serve to facilitate the exchange of information between researchers and industry professionals to discuss the latest issues and
advancement in the area of advances.

La connessione fra logica ed ontologia si puó cogliere in maniera il piú possibile precisa osservando una teoria formalizzata. In tal caso l’ontologia relativa a tale teoria è da intendersi, da un punto di vista sintattico, una teoria delle forme logiche, in quanto ha per oggetto i modi di combinare le categorie logico-grammaticali del linguaggio (formale) adottato da tale teoria. In tal modo, agendo su di esse, si puó definire e osservare il comportamento formale di tali forme e in funzione dell’ontologia che si vuole supporre in una data teoria. La definizione delle forme logiche di una teoria non é affidata all’apparato descrittivo, specifico della teoria formalizzata di cui si è in possesso – che sia l’apparato linguistico (le costanti non-logiche), che sia quello assiomatico (gli assiomi e le definizioni non-logici). Quali sono le categorie ontologiche supposte da una specifica teoria e il modo in cui è regolato il loro comportamento  dipende strettamente dalla struttura logica della teoria: mediante le distinzioni in categorie, appunto, logico-grammaticali: mediante la stipulazione delle regole e degli assiomi logici, si controllano le possibili trasformazioni simboliche fra queste categorie. A variazioni relative a tali trasformazioni corrispondono variazioni dell’ontologia di riferimento per la teoria.
In questo lavoro ci concentreremo sulle differenze fra realismo e nominalismo descritte e controllate all’interno della logica matematica, della logica classica del primo e del secondo ordine per le quali rimandiamo a (Enderton 2001)

International Journal on Foundations of Computer Science & Technology (IJFCST) is a Bi-monthly peer-reviewed and refereed open access journal that publishes articles which contribute new results in all areas of the Foundations of Computer Science & Technology. Over the last decade, there has been an explosion in the field of computer science to solve various problems from mathematics to engineering. This journal aims to provide a platform for exchanging ideas in new emerging trends that needs more focus and exposure and will attempt to publish proposals that strengthen our goals. Topics of interest include, but are not limited to the following:

Abstract. Domain ontology building is one of the most critical activities required in Semantic Web applications. The task must be performed by domain experts, who do not (generally) have the background of a knowledge engineer. To ease this task, Ontology Management Systems (such as Kaon, Protégé, OntoEdit, Athos) are developing user friendly interfaces. However the problem is mainly of a cognitive nature. Difficulties comes from the fact that the existing ontology languages: (i) are hard to be used by unskilled people, (ii) have very basic constructs (e.g., class, property), (iii) are not domain specific, i.e., they are conceived for very diverse contexts (e.g., from medical sector to high energy physics). OPAL (Object, Process, Actor modelling Language) aims at supporting business experts who need to build an ontology by providing a limited number of high level conceptual templates.

The aim of this project was to discover and extract the Evolutionary Algorithms in a Fortune-telling document attributed to Shaikh Bahaʼi. This document accounts for a model of formal languages where there exists accurate and proportionate relationships between the symbolic systems of Language and Mathematics. This systematic relationship increases the face complexity of the document while it eases the access to the final response quickly and easily. The alphabets using through the tables are the letters of Persian alphabet, not the Abjad alphabets. By studying the tables and extracting the mathematical relations between the letters and the numbers, the arrangement and gaining response mechanisms of the document are shown. They are compatible with EA model...

Expressions in natural language, especially in technical texts, can be regarded as expressions of relations between related things. Each related thing plays a role of a particular kind in such as relation, whereas also the relations can be classified by kinds of relations. By formally defining such kinds of relations as part of the definition of a formal language it becomes possible to create a formal language that is suitable for expressing information in databases, data exchange messages as well as queries on such data and responses of found expressions. The kinds of relations can be arranged in a strict subtype-supertype hierarchy, also called a taxonomy. That hierarchy enables application of logic and reasoning for finding answers on queries. This paper describes the taxonomic dictionary of relations in Gellish Formal English and its variants in other languages. The dictionary of (kinds of) relations itself is published in book form [Ref. ‎ 6], the more extensive formal definition and ontology in database form is available only in electronic form via Gellish.net.

Original version of my PhD dissertation (University of Reading), a much shorter version of which (~ 60% shorter) was defended on 1/2018.

This work is a study of the nature of cognitive computation, with a focus on the relation between computation, linguistic theory, and grammar. We review traditional notions of computation and analyse their applicability to natural language, distinguishing the latter from formal languages as these are usually studied in computer science.
The main theoretical result of the thesis is that imposing a single computational template for the assignment of structural descriptions to natural language sentences, while long accepted, is both empirically inadequate and theoretically more costly than a strongly cyclic approach in which computational dependencies vary, oscillating up and down the Chomsky Hierarchy of formal grammars. Specifically, we defend the idea that such a system delivers the simplest possible structural description that captures semantic dependencies between syntactic objects in local substrings. This hypothesis will be referred to as the theory of mixed computation. The analysis of theories of computation starting with the seminal work of Alan Turing (1936) will reveal that the theory of computable functions must not be identified with the theory of effective computation; this then permits us to argue for the necessity of introducing aspects of interaction in the study of physically realized computational procedures which configure dynamical systems. We show that mixed computation lends itself naturally to modelling dynamical systems.
Empirically, we present evidence for mixed computation derived from an analysis of strong locality conditions in natural language syntax, that is, locality constraints whose violation cannot be repaired or ameliorated. Specifically, we set our focus on the Coordinate Structure Constraint (Ross, 1967), which pertains to the extraction of terms from coordinated structures and how it can be shown to arise from a mixed-computation analysis. Data from English, Spanish, and Latin support the identification of two kinds of coordinated structures: one is finite state in nature, and cannot be probed into. The other is phrase structural (context-free), and its internal complexity is visible to further syntactic operations, including extraction. We argue that data from locality conditions as well as cyclicity in natural-language syntax are accounted for naturally under a dynamical model of mixed computation.

In some contexts, especially in safety or security critical applications, it may be crucial to verify that the interactive behaviour of these systems possess certain formally expressed properties. Our project is to describe the interactive behaviour of a system by building an abstract formal model of it and to verify automatically that this behaviour possesses the required properties. In this paper, we suggest to use data flows for this purpose. We use the formal language Lustre to denote such flows. This language permits to express safety temporal properties and to build some syntactical structures in order to verify and test them by using appropriate tools.

La teoría de autómatas, también llamada teoría algebraica de máquinas, permite estudiar de un modo sistemático las máquinas, más o menos complicadas, que realizan un procesamiento de la información y que actúan de manera discreta; es decir, la información se supone codificada a partir de un conjunto finito de símbolos que el autómata trata secuencialmente, uno detrás de otro. La teoría de autómatas proporciona métodos para el análisis y la síntesis de tales máquinas. Los trabajos sobre lenguajes y gramáticas formales han evolucionado en una dirección que les ha conducido a encontrarse con la teoría de autómatas como herramienta matemática de gran utilidad. Este artículo pretende ser una introducción básica a dicha teoría de autómatas.

Until now, the results about "contextual automata" is reduced to a single example that characterise a more specific class of contextual language. The definition of new types of automata which characterise the other contextual languages is considered an "open problem". In this article we present the state of the art in the field of contextual automata.

International Journal on Foundations of Computer Science & Technology (IJFCST) is a Bi-monthly peer-reviewed and refereed open access journal that publishes articles which contribute new results in all areas of the Foundations of Computer Science & Technology. Over the last decade, there has been an explosion in the field of computer science to solve various problems from mathematics to engineering. This journal aims to provide a platform for exchanging ideas in new emerging trends that needs more focus and exposure and will attempt to publish proposals that strengthen our goals. Topics of interest include, but are not limited to the following

We consider internal contextual grammars (with finite and with regular selection sets) with the derivation restricted in the following way: when a word is used as a selector, then no subword/superword of it can be used as a selector. This can be considered both locally (with respect to the chosen selection set) or globally (with respect to all selection sets). The generative capacity of such grammars is investigated (comparing each other the above mentioned variants and with the class of unrestricted internal contextual grammars). Finally, grammars with selectors checked as scattered subwords of the derived words are considered.

Motivated by a study of similar problems stated for factors of words, we study forbidden subwords of a language or a word. A procedure for obtaining the set of all words avoiding a given set of subwords is presented. On the other hand, an algorithm for computing the set of minimal forbidden subwords for a word is given. The case of a two-letter alphabet appears to be particularly interesting and it is considered separately.

In this work we will analyze some recent proposals about how the result of the application of a generative algorithm is recognized as a unit for the purposes of further computations, and how each correlates, either explicitly or implicitly, with a model of the mind. We will propose, in line with previous works, that a mixed approach to mental computations (including both Markovian and non-linear dependencies) can prove useful at both theoretical and empirical levels when stated explicitly. We will argue that phrase markers include both kinds of dependencies between terminals and non-terminals: labeling requirements in a theory (which, in turn, interact with other conditions on phrase structure, binarity being the most notable) give away the conception a certain theory has about the (uniform or not) functioning of the mind.

Los modelos algebraicos analíticos del lenguaje aparecieron en los años 60 del sigo XX. Sus fundamentos fueron lingüísticos, matemáticos, lógicos y computacionales. Los modelos analíticos se relacionan con con las propiedades internas, intrínsecas de los lenguajes (relaciones entre las subcadenas de una cadena dada, posibilidades de substituir una cadena por otra en un contexto dado, etc.). La primera visión sistemática de los modelos analíticos apareció en monografías de S. Marcus en 1967; pero dicha visión fue ampliamente superada en los últimos 25 años del siglo XX por nuevas aportaciones al respecto. Desafortunadamente este ámbito de investigación fue y sigue siendo ignorado por muchos/as investigadores/as en lingüística formal y computacional. Sin embargo, algunos modelos analíticos algebraicos (por ejemplo, las Gramáticas Contextuales) poseen un gran potencial para capturar diversos fenómenos en el ámbito de la sintaxis y la semántica de los lenguajes naturales, en la representación del conocimiento, en la inteligencia artificial, en las acciones humanas, y en otros tipos de ámbitos relacionados con las competencias humanas, los lenguajes de programación, etc.

Cet article se propose de discuter l’idée, aujourd’hui répandue, que les ontologies fondationnelles sont utiles, voire nécessaires, pour assurer l’interopérabilité sémantique entre systèmes de collecte de données faisant usage de terminologies hétérogènes, c’est-à-dire pour résoudre le problème dit de la Tour de Babel. Après un rappel des principales caractéristiques des ontologies, nous proposons une liste des grandes fonctions généralement attribuées, et a minima attendues des ontologies fondationnelles, pour en discuter ensuite le bien-fondé. Nous montrons (i) que la possibilité de réaliser une ontologie intégrant des primitives et définitions formelles suffisamment universelles pour décrire la sémantique des concepts de domaines spécialisés du savoir est loin d’être acquise ; (ii) que même si une telle ontologie s’avérait réalisable, il n’est pas certain qu’elle permettrait d’assurer l’interopérabilité sémantique entre systèmes de données hétérogènes, c’est-à-dire un échange de données préservant le sens que ces données possèdent pour ceux qui les ont encodées.