Formal System and Semantics of NΣ-Labeled Calculus

Author(s):  
Y. Ikeda ◽  
T. Mizutani ◽  
M. Shio
Keyword(s):  
2019 ◽  
Vol 28 (1) ◽  
pp. 19-27
Author(s):  
Ja. O. Petik

The connection of the modern psychology and formal systems remains an important direction of research. This paper is centered on philosophical problems surrounding relations between mental and logic. Main attention is given to philosophy of logic but certain ideas are introduced that can be incorporated into the practical philosophical logic. The definition and properties of basic modal logic and descending ones which are used in study of mental activity are in view. The defining role of philosophical interpretation of modality for the particular formal system used for research in the field of psychological states of agents is postulated. Different semantics of modal logic are studied. The hypothesis about the connection of research in cognitive psychology (semantics of brain activity) and formal systems connected to research of psychological states is stated.


1993 ◽  
Vol 19 (3-4) ◽  
pp. 275-301
Author(s):  
Andrzej Biela

In this paper we shall introduce a formal system of algorithmic logic which enables us to formulate some problems connected with a retrieval system which provides a comprehensive tool in automated theorem proving of theorems consisting of programs, procedures and functions. The procedures and functions may occur in considered theorems while the program of the above mentioned system is being executed. We can get an answer whether some relations defined by programs hold and we can prove functional equations in a dynamic way by looking for a special set of axioms /assumptions/ during the execution of system. We formulate RS-algorithm which enables us to construct the set of axioms for proving some properties of functions and relations defined by programs. By RS-algorithm we get the dynamic process of proving functional equations and we can answer the question whether some relations defined by programs hold. It enables us to solve some problems concerning the correctness of programs. This system can be used for giving an expert appraisement. We shall provide the major structures and a sketch of an implementation of the above formal system.


2021 ◽  
Vol 179 (2) ◽  
pp. 93-111
Author(s):  
Ludwik Czaja

Cause-effect structures are objects of a formal system devised for modeling, testing and verifying properties of tasks, where parallel execution of actions is the most characteristic feature. This is an algebraic system called a quasi-semiring. In this paper elementary cause-effect structures, a system behaviourally equivalent to 1-safe Petri nets, are extended by the following features: weighted edges, multi-valued nodes having capacities (counterpart of place/transition Petri nets), inhibitors and a model of time. The extensions are accomplished by modifying the notion of state and semantics, but leaving unchanged structure of the quasi-semiring expressions.


1984 ◽  
Vol 7 (3) ◽  
pp. 359-365
Author(s):  
Dymiter Skordev

The paper presents an abstract tool for describing general properties of programs. Iterative combinatory space approach makes possible to transfer recursion – theoretical methods onto logical system which is constructed in this paper.


2010 ◽  
Vol 50 (1) ◽  
pp. 665
Author(s):  
Ally Oliver

A permit to work (PTW) system is a formal system used to control certain types of work that are identified as potentially hazardous. It is also a means of communication between facility management, plant supervisors and operators, and those who carry out the hazardous work. The essential features of a PTW system are: • Clear identification for who may authorise particular jobs, and who is responsible for specifying the necessary precautions; • Training and instruction in the issue and use of permits; and, • Monitoring and auditing to ensure that the system works as intended. PTW systems are the key to ensuring safe execution of activities at site, yet there are many approaches to how permit systems can, and should, work. Each approach has its own merits and weaknesses. Woodside recognised that, as part of its ongoing program to improve the safety of its workers, there existed significant scope for a new and better work management system. After many years of incremental evolution of the PTW and the fragmentation of the parent system as each facility developed its own variation, it was evident that a completely new system embracing modern technology would provide the best result, while simultaneously standardising Woodside with one common and centralised system. The divergence of the systems over time caused increasing difficulty in managing changes to the PTW system across all sites and in benchmarking to determine best practice. A centralised system would remove accountability from facilities for the development of the business rules, and instead ensure they focussed on compliance with the rules. The new system would adopt key learnings from the industry’s history and address root causes of past incidents. It would also enable the ability to adopt future learnings and become a conduit for rapid integration into the working practices on all sites. The Integrated Safe System of Work (iSSoW) developed by Woodside adopts best practices from permit systems worldwide and combines them with new innovative management features. The system is administered through a simple-to-use computer interface, with incorporation of many of the business rules into the software package. The iSSoW is now in place on all Woodside facilities (platforms, not-normally manned installations, FPSO’s and onshore plants). With nearly 4,000 users, the implementation has required careful coordination, and been supported by a comprehensive training programme. The system has been demonstrated to be both effective and efficient. Effectiveness—the improvement of safety performance—was the primary objective. The system has raised work party hazards awareness, and has resulted in significant improvements in working practices company-wide. Efficiency was a secondary goal, and is made possible through streamlining in the user-interface. The introduction of the new system complements Woodside’s work to develop an improved safety culture, and brings consistency across all sites and all shifts—essential features as our industry struggles to deal with the growing scarcity of skills and experience. The system is now being reviewed by organisations across many industry and service sectors in Australia, and has been implemented in the power industry. This paper discusses the attributes of the system, the many challenges associated with development and large-scale implementation of such a core system, and the additional opportunities the system presents. Using a case study of implementation of iSSoW onto the Woodside operational facilities, it highlights the critical success factors of introducing iSSoW on a company-wide basis.


2010 ◽  
Vol 3 (2) ◽  
pp. 262-272 ◽  
Author(s):  
KLAUS GLASHOFF

Since Frege’s predicate logical transcription of Aristotelian categorical logic, the standard semantics of Aristotelian logic considers terms as standing for sets of individuals. From a philosophical standpoint, this extensional model poses problems: There exist serious doubts that Aristotle’s terms were meant to refer always to sets, that is, entities composed of individuals. Classical philosophy up to Leibniz and Kant had a different view on this question—they looked at terms as standing for concepts (“Begriffe”). In 1972, Corcoran presented a formal system for Aristotelian logic containing a calculus of natural deduction, while, with respect to semantics, he still made use of an extensional interpretation. In this paper we deal with a simple intensional semantics for Corcoran’s syntax—intensional in the sense that no individuals are needed for the construction of a complete Tarski model of Aristotelian syntax. Instead, we view concepts as containing or excluding other, “higher” concepts—corresponding to the idea which Leibniz used in the construction of his characteristic numbers. Thus, this paper is an addendum to Corcoran’s work, furnishing his formal syntax with an adequate semantics which is free from presuppositions which have entered into modern interpretations of Aristotle’s theory via predicate logic.


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