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Towards Conceptual Modeling Semantics: Eventizing Tarski's Truth

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Towards Conceptual Modeling Semantics: Eventizing Tarski's Truth IJCSNS International Journal of Computer Science and Network Security, VOL.20 No.10, 223-233, October 2020 Towards Conceptual Modeling Semantics: Eventizing Tarski’s Truth Schema Sabah Al-Fedaghi [email protected] Computer Engineering Department, Kuwait University, Kuwait problem [2]. In the case of UML, the language evolved Summary from software systems modeling where denotational Modeling languages in software engineering (e.g., UML) (using mathematical objects) and operational (using evolved from software systems modeling where execution) kinds of semantics are the traditional subjects denotational and operational kinds of semantics are the of research and practice [3-4]. According to Ekenberg and traditional subjects of research and practice. According to Johannesson [5], work on formalizing UML has attempted some authors, although a large portion of the static to use different versions of temporal logic (see, e.g. [6-7]). semantics (e.g., UML) seems to have reached a consensus, Dynamic logic has also been used as a basis for UML the dynamic semantics of activities, interactions, and state semantics (e.g., in [8-9]). In 2020, OMG [10-11] released machines poses a major challenge. Central to semantics is a draft specification of Foundational UML (fUML) the relationship between a sentence and the (actual) world. wherein basic semantics specify when particular Carefully examining semantics-related issues in the executions conforming to a model defined in fUML modeling languages field to avoid problems that may affect practical applicability is important. One effort in this generate executions. As a specification, fUML has direction is OMG‟s release of a 2020 draft specification standard, precise execution semantics. It is a subset that for Foundational UML (fUML), with the base semantics includes constructs of UML and the ability to model specifying executions that are executable in the same sense behavior using a composed set of primitive actions. A as a program in a traditional programming language. model constructed in fUML is “executable in exactly the Additionally, efforts within academia have sought to same sense as a program in a traditional programming develop an alternative approach to modeling languages language, but it is written with the level of abstraction and using formal semantics (e.g., using Russell‟s theory of richness of expression of a modeling language” [12]. types and Tarski‟s declarative semantics). This paper aims According to Broy et al. [13], although a large portion of at a similar exploratory venture of developing semantics, the static semantics of UML seem to have reached a only for a much more modest diagrammatic modeling consensus, the dynamic semantics of the UML language, called the thinging machine model. The model sublanguages, such as activities, interactions, and state promotes a deep understanding of the scrutinized modeling machines, pose a major challenge. These foundational language and leads to considerably fruitful questions. difficulties involving dynamic semantics of such tools as Constructing the thinging machine model seems to state machines lead to definitions that contradict common facilitate progress in this direction, and the initial results in sense [13]. They “show how important it is to carefully this paper indicate the viability of the approach. design a modeling language to avoid problems regarding Key words: its expressivity as well as its interpretation—problems that Conceptual modeling, modeling language, diagrammatic strongly impact practical applicability [13]. Efforts within representation, formal semantics, UML semantics, T-schema academia have sought to develop an alternative approach to UML‟s formal semantics (e.g., using Russell‟s theory of 1. Introduction types and Tarski‟s declarative semantics [1-4]). Diagrammatic modeling languages (e.g., UML) have 1.1 Aim become the key artifacts of software development, and This paper aims at a first step toward developing “the solidness of modeling languages metamodels” has semantics, only for a much more modest diagrammatic generated important outcomes in the field of software modeling language called the thinging machine (TM). engineering [1]. They are proving extremely helpful in According to Broy et al. [13], formalization is a scientific software and systems development. However, when approach that promotes deep understanding of different formal semantics (meaning in contrast to syntax) are called aspects of the scrutinized modeling language. Trying to for, properly defining diagrams seems to be a much harder conduct the formalization uncovers many properties of the Manuscript received October 5, 2020 Manuscript revised October 20, 2020 2 IJCSNS International Journal of Computer Science and Network Security, VOL.20 No.9, September 2020 modeling language and leads to considerably fruitful expression of the classical correspondence theory. This questions. In this paper, we explore a new territory in logic conception was done in linguistic terms that are supposed as much as in modeling though investigation of the notion to refer to objects in the world. Our basic idea is to “inject” of truth and hence the semantics for relations among the the diagrammatic form as follows: concepts and the subject that is being modeled in the TM “p” is true if, and only if, B (i.e., iff the corresponding context. chronology of events holds) 1.2 Justification where B is the chronology of events expressed as a diagrammatic construct. This form is generalized for S, The paper suggests applying logical semantics to the and hence, if S is true, then so is B. Although such a form diagrammatic method used in conceptual modeling. The of representation does not bring a new idea to Tarski‟s T justification for this direction of research is that the schema, it weakens its reliance on textual language reliance on graphical constructs poses problems when it because B is specified as a diagrammatic expression. comes to precise and unambiguous semantics [5]. The To achieve a self-contained paper, the next section reviews first-order logic, when used in conjunction with conceptual the TM model. A more elaborate discussion of the TM modeling, “provides a sound basis on which specifications model‟s foundations can be found in [18-29]. written in a process-based language can be transformed, merged, and verified for the purpose of detecting interference” [5]. Additionally, logic-based formalization 2. The TM Model provides support for tasks by means of logic-based inference (a topic not discussed in this paper) so that tools The main TM thesis is that each entity has a double nature can provide effective support for automated reasoning as (i) a thing and (ii) a process (abstract machine); thus, we [14]. call these thing/machine entities thimacs. In TM modeling, intertwining with the world is accomplished by integrating Diagramming has been used in logic for various reasons. these two modes of being of entities. Thimacs inhibit the Besides the use of diagrams as illustrations or thought traditional categorization, properties, and behavior, aids, diagrammatic systems have also formalized logic. replacing them with creating, processing, releasing, These include Frege‟s [15] Begriffsschrift (“conceptual transferring, and receiving. Such a thesis has profound notation”) and Charles Sanders Peirce‟s [16] existential influence on the semantics of TM modeling of the world. graphs. It implies that all actions are reduced to five actions or generic (elementary) machines. Because machines are 1.3 Outline things, all things can be reduced to five elementary things: TM modeling is a three-level process that involves the the create thing, the process thing, the release thing, the following: transfer thing, and the receive thing. These ideas were A static model of the state of affairs to produce an inspired by and can be traced back to Aristotle in ancient atemporal diagrammatic description denoted as S. history and Heidegger in modern times (see [29]). As A decomposition of S into subdiagrams that form the stated in Al-Fedaghi [29], Aristotle proclaimed entities are base of temporal events. the sorts of “basic beings that fall below the level of truth- makers, or facts, just as … nouns and verbs, things said The behavior of the model, denoted as B, is „without combination,‟ contribute to the truth-evaluability formulated as a chronology of events. The behavior of simple assertions” [30]. Moreover, Aristotle introduced refers to executing composite actions. the notion of process in thinking about things. He conjectured that a thing in nature persists via an internal We try to clarify the intuitive conception of the TM process that must be realized within a matter that harbors diagrammatic representation by incorporating the tendencies resulting from its elemental components (e.g., semantics notion of logical consequence. The fundamental fire, water, earth, or air). This causes tendencies to actively idea is that the semantics are built upon B (chronology of strive toward their “natural place.” In this view, Aristotle permitted events). can be counted as a process philosopher [31]. Aristotle‟s Thus, consider a given statement p, in terms of Tarski‟s idea is that things are compounds consisting of matter and famous T(ruth) schema [17]: form. According to Heidegger [32], a thing is self- “p” is true if and only if P. (i.e., iff the corresponding state of affairs holds) sustained, self-supporting, or independent—something that stands on its own. The condition of being self-supporting The T schema can be formalized in many-sorted predicate transpires by means of producing the thing. Heidegger [32] logic or modal logic. Tarski conceived the T schema as an IJCSNS International Journal of Computer Science and Network Security, VOL.20 No.10, October 2020 3 encourages further research on “generic processes” applied 3. TM Modeling to a thing. Klimek [33] dealt with the problem of the lack of tools for Accordingly, in this paper, we claim that mapping to the automatic extraction of logical specifications from “object world” can be accomplished by mapping the five software models and proposed a method for automatic generic thimacs.
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