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Ontological Structures for Higher Levels of Distributed Fusion
Published in David L. Hall, Chee-Yee Chong, James Llinas, Martin Liggins, Distributed Data Fusion for Network-Centric Operations, 2013
Mieczyslaw M. Kokar, Brian E. Ulicny, Jakub J. Moskal
Logical inference is possible within a formal system, i.e., a system that includes a formal language, a theory (or axioms), and inference rules. Formal language is a language that has formal syntax and formal semantics. Formal syntax means rules for determining whether a given expression is in the language or not (sometimes referred to as legal sentences or well-formed formulas). Formal semantics refers to interpretations, which are mappings from the language to a mathematical domain (a set of individuals) and from sentences to truth values. Theories are then represented by axioms—sets of sentences in the language. Inference rules are rules that can be applied to the axioms of a theory to derive new sentences, which then become part of the theory. A formal system should be sound, i.e., given a consistent set of true sentences, it derives only true sentences, i.e., sentences that map to the value “true” by the interpretation function. Another desirable, but unachievable, feature of a formal system is completeness, i.e., the ability to infer all possible true sentences using the rules of inference.
Introduction
Published in John N. Mordeson, Davender S. Malik, Fuzzy Automata and Languages, 2002
John N. Mordeson, Davender S. Malik
The customary Chomsky hierarchy of formal languages is obtained by imposing restrictions on the form of the rewriting rules, i.e., productions. In certain grammars, an application of some production determines which productions are applicable on the next step. These are called programmed grammars. In ordered grammars, some productions can never be applied if some others are applicable. In matrix grammars, only certain previously specified strings of productions can be applied or, more generally, in a grammar with a control set, the string of productions corresponding to a derivation must belong to a set of strings previously specified. See, for example, [185,61,1,80]. We consider time variant and probabilistic grammars.
Logic
Published in Jay Liebowitz, The Handbook of Applied Expert Systems, 2019
As a mathematical structure, logic is characterized by the following three components: a formal language in which knowledge can be expressed, a semantics to give meaning to the sentences of the language, and proof procedures to infer knowledge. A formal language is denned by a syntax that uses an alphabet of symbols and defines rules to combine the elements of the alphabet to form sentences called well-formed formulae. Symbols of the alphabet include constants, variables, functions, predicates, and connectives.
Production processes modelling within digital product manufacturing in the context of Industry 4.0
Published in International Journal of Production Research, 2023
Marko Vještica, Vladimir Dimitrieski, Milan Mirko Pisarić, Slavica Kordić, Sonja Ristić, Ivan Luković
The MasL model enrichment, i.e. creating a DetL model, may be performed manually by a process engineer utilising Modelling Tool. Enrichment of MasL models may also be performed automatically by the Orchestrator software component (see Figure 1), creating DetL models. Although manual creation of DetL models is possible, it would be a complex task as it requires knowledge of all the technological and production system details needed to execute the process. Therefore, the full potential of our system is reached if Orchestrator is used to automating this burdensome process. Once created, DetL models can be used to generate resource instructions to execute process operations. Regardless of how DetL models are created, they can be manually refined and optimised before instruction generation by process engineers if deemed necessary. Orchestrator does not interpret the graphical representation of a process flow. Instead, models are transformed into instructions via formally defined transformation rules, i.e. generators. As MultiProLan is created to be a formal language with exact and precise semantics, modelling concepts are machine-readable and understandable, enabling the automatic transformation of modelling concepts into instructions to execute process operations.
Measuring Austrian students’ procedural knowledge at the end of upper secondary level
Published in International Journal of Mathematical Education in Science and Technology, 2023
Christoph Ableitinger, Christian Dorner
There are different conceptualisations for procedural knowledge in the literature. In particular, the formulations of Star et al. (2015, p. 45): ‘Procedural knowledge refers to having knowledge of action sequences for solving a problem’ and Rittle-Johnson and Schneider (2014, p. 5): ‘[…] procedural knowledge is the ability to execute action sequences (i.e. procedures) to solve problems’ reflect a certain duality of this knowledge type. On the one hand, procedural knowledge includes the knowledge of the procedure, which usually relates to specific procedures. On the other hand, the concrete execution of the procedure requires mathematical skills that can be used in a wide variety of mathematical topics (Altieri, 2016; Dorner & Ableitinger, 2022). Altieri (2016) takes this duality into account by bringing the two aspects together and combining them in a common definition: Knowledge of the procedure: Knowledge of symbols and the formal language of mathematics as well as knowledge of rules and procedures for solving mathematical problems.Procedural skills: Skills required to apply the knowledge of the procedure in a case-specific and targeted manner in a way that leads to a correct result in a reasonable time, especially in the case of procedures. (Altieri, 2016, p. 25; translation from Dorner & Ableitinger, 2022, p. 4)
Assisting academics to identify computer generated writing
Published in European Journal of Engineering Education, 2022
El-Sayed Abd-Elaal, Sithara H.P.W. Gamage, Julie E. Mills
During the training, it was highlighted that AAG is an online computer program that has access to a large database including old and new academic articles, reports, books, newspaper, web pages, etc. These programs search the databases according to the provided keywords, or the title of the proposed research and then they compose the related articles in the required style. These article generators utilise jargon (Jargon refers to special terminologies which are specific to a particular research area, and may not be well understood outside that context) from the related field to compose sentences. Researchers have found that jargon can deceive the inexperienced reader (Kelly-Bootle 2005). These computer programs also use context-free grammar tools (a set of grammar rules used to create patterns of strings in a formal language). By using context-free grammar tools plus features to replace a bit of the articles’ contents with random synonyms, the resultant writing will not be a direct copy from published work and thus plagiarism detection tools cannot detect this fabrication. Furthermore, ‘generating natural language techniques’, which provides wording very close to human-crafted phrases, may be implemented in these tools. The information gathered from the literature was presented in the training. The summary slide used in the training is shown in Figure 2.