scholarly journals Aristotle and Boethius: Two Theses and Their Possibilities

Author(s):  
Miguel López-Astorga

There is a kind of logical theses that can be a cognitive problem. They are theses that are not tautologies and people tend to accept as absolutely correct. This is the case of theses such as those of Aristotle and Boethius. This paper tries to give an explanation of the reasons why this happens. The explanation is based on the theory of mental models. However, it also resorts to modal logic and the account of the ideas presented by Lenzen. Thus, relating the general framework of the theory of mental models to basic aspects of modal logic and this last account, a possible solution of the problem is proposed.

2019 ◽  
Vol 29 (8) ◽  
pp. 1344-1378
Author(s):  
TOMER LIBAL ◽  
MARCO VOLPE

One of the main issues in proof certification is that different theorem provers, even when designed for the same logic, tend to use different proof formalisms and produce outputs in different formats. The project ProofCert promotes the usage of a common specification language and of a small and trusted kernel in order to check proofs coming from different sources and for different logics. By relying on that idea and by using a classical focused sequent calculus as a kernel, we propose here a general framework for checking modal proofs. We present the implementation of the framework in a Prolog-like language and show how it is possible to specialize it in a simple and modular way in order to cover different proof formalisms, such as labelled systems, tableaux, sequent calculi and nested sequent calculi. We illustrate the method for the logic K by providing several examples and discuss how to further extend the approach.


1966 ◽  
Vol 31 (1) ◽  
pp. 46-65 ◽  
Author(s):  
E. J. Lemmon

Modal logic received its modern impetus from the work of Lewis and Langford [10]. In recent years, however, their axiomatic approach, aided by somewhat ad hoc matrices for distinguishing different modal systems, has been supplemented by other techniques. Two of the most profound of these were, first, the algebraic methods employed by McKinsey and Tarski (see [11] and [12]) and, second, the semantic method of Kripke (see [5] and [6]); and there have been others. The aim of the present series of papers is to afford a synthesis of these methods. Thus, though new results are given, the interest lies rather in revealing interconnexions between familiar results and in providing a general framework for future research. In general, we show that semantic completeness results of the Kripke kind can be deduced from the algebraic results by means of one central theorem (Theorem 21).


1989 ◽  
Vol 33 (5) ◽  
pp. 350-350
Author(s):  
Deborah A. Mitta

Expert system knowledge represents expertise obtained through formal education, training, and/or experience. Formal education provides deep knowledge of a particular domain; experience and training result in heuristic knowledge. A knowledge base defines the range of information and understanding with which the system is capable of dealing; therefore, its information must be structured and filed for ready access. The objective of this symposium is to address the challenges associated with establishment of valid expert system knowledge, specifically, knowledge to be used by expert system shells. As expert system knowledge is obtained, structured, and stored, it is formulated. In this symposium, knowledge formulation is addressed as a three-phase process: knowledge acquisition, the mechanics associated with structuring knowledge, and knowledge porting. Knowledge acquisition is the process of extracting expertise from a domain expert. Expertise may be collected through a series of interviews between the expert and a knowledge engineer or through sessions the expert holds with an automated knowledge acquisition tool. Thus, the ultimate outcome of knowledge acquisition is a collection of raw knowledge data. The following human factors issues become apparent: documenting mental models (where mental models are the expert's conceptualization of a problem), recording cognitive problem-solving strategies, and specifying an appropriate interface between the domain expert and the acquisition methodology. The knowledge structuring process involves the refinement of raw knowledge data, where knowledge is organized and assigned a semantic structure. One issue that must be considered is how to interpret knowledge data such that formal definitions, logical relationships, and facts can be established. Finally, formulation involves knowledge porting, that is, the movement of an expert system shell's knowledge base to various other shells. The outcome of this process is a portable knowledge base, where the challenges lie in maintaining consistent knowledge, understanding the constraints inherent to a shell (the shell's ability to incorporate all relevant knowledge), and designing an acceptable user-expert system interface. The fundamental component of any expert system is its knowledge base. The issues to be presented in this symposium are important because they address three processes that are critical to the development of a knowledge base. In addition to presenting computer science challenges, knowledge base formulation also presents human factors challenges, for example, understanding cognitive problem-solving processes, representing uncertain information, and defining human-expert system interface problems. This symposium will provide a forum for discussion of both types of challenges.


2020 ◽  
Vol 57 (3) ◽  
pp. 75-86
Author(s):  
Miguel Lopez-Astorga ◽  

The mental models theory is a current approach trying to account for human thought and hence communication by highlighting the action of semantics and ignoring, to a large extent, syntax. However, it has been argued that the theory actually contains an underlying syntax related to any kind of modal logic. This paper delves into this last idea and is intended to show that the concepts of possibility and necessity as understood in it fulfill the basic requirement that, according to Fitting and Mendelsohn, every modal logic has to meet: to satisfy the relationships provided by the Aristotelian modal square of opposition.


1989 ◽  
Vol 33 (5) ◽  
pp. 351-355 ◽  
Author(s):  
Deborah A. Mitta

Knowledge acquisition is the process of extracting expertise from a domain expert. Expertise may be collected manually via a series of interviews held between the expert and a knowledge engineer or through sessions the expert holds with an automated knowledge acquisition tool. Several human factors issues become apparent: documenting mental models (where mental models are the expert's conceptualization of a problem), recording cognitive problem-solving strategies, and specifying an appropriate interface between the domain expert and the acquisition methodology. This paper provides a discussion of current manual/automated acquisition techniques, human factors issues associated with knowledge acquisition, and the ways in which several acquisition methodologies have confronted human factors issues.


Author(s):  
Brian F. Chellas
Keyword(s):  

Author(s):  
Burkhard Müller ◽  
Jürgen Gehrke

Abstract. Planning interactions with the physical world requires knowledge about operations; in short, mental operators. Abstractness of content and directionality of access are two important properties to characterize the representational units of this kind of knowledge. Combining these properties allows four classes of knowledge units to be distinguished that can be found in the literature: (a) rules, (b) mental models or schemata, (c) instances, and (d) episodes or chunks. The influence of practicing alphabet-arithmetic operators in a prognostic, diagnostic, or retrognostic way (A + 2 = ?, A? = C, or ? + 2 = C, respectively) on the use of that knowledge in a subsequent test was used to assess the importance of these dimensions. At the beginning, the retrognostic use of knowledge was worse than the prognostic use, although identical operations were involved (A + 2 = ? vs. ? - 2 = A). This disadvantage was reduced with increased practice. Test performance was best if the task and the letter pairs were the same as in the acquisition phase. Overall, the findings support theories proposing multiple representational units of mental operators. The disadvantage for the retrognosis task was recovered in the test phase, and may be evidence for the importance of the order of events independent of the order of experience.


1992 ◽  
Vol 37 (5) ◽  
pp. 438-439
Author(s):  
Richard A. Griggs
Keyword(s):  

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