Mathematical-Semantics, psychology and super-psychological Idealizations: a proposal for a non-dogmatic reading of semantic theories

2021 ◽  
Author(s):  
Lucas Ribeiro Vollet
Keyword(s):  
Mathematical Semantics

A Two-Part Defense of Intuitionistic Mathematics

2021 ◽  
Vol 14 ◽  
pp. 26-38
Author(s):  
Samuel R. Elliott ◽  
Keyword(s):  
Alternative Interpretation ◽  
Alternative Conception ◽  
Suitable Candidate ◽  
Michael Dummett ◽  
Intuitionistic Mathematics ◽  
Mathematical Semantics

The classical interpretation of mathematical statements can be seen as comprising two separate but related aspects: a domain and a truth-schema. L. E. J. Brouwer’s intuitionistic project lays the groundwork for an alternative conception of the objects in this domain, as well as an accompanying intuitionistic truth-schema. Drawing on the work of Arend Heyting and Michael Dummett, I present two objections to classical mathematical semantics, with the aim of creating an opening for an alternative interpretation. With this accomplished, I then make the case for intuitionism as a suitable candidate to fill this void.

scholarly journals Vicious Circle Principle and Logic Programs with Aggregates

2014 ◽  
Vol 14 (4-5) ◽  
pp. 587-601 ◽  
Author(s):  
MICHAEL GELFOND ◽  
YUANLIN ZHANG
Keyword(s):  
Knowledge Representation ◽  
Vicious Circle ◽  
Logic Programs ◽  
Vicious Circle Principle ◽  
Knowledge Representation Language ◽  
Representation Language ◽  
Answer Sets ◽  
Mathematical Semantics

AbstractThe paper presents a knowledge representation language $\mathcal{A}log$ which extends ASP with aggregates. The goal is to have a language based on simple syntax and clear intuitive and mathematical semantics. We give some properties of $\mathcal{A}log$, an algorithm for computing its answer sets, and comparison with other approaches.

Semantics and Pragmatics in Mathematical Events

2018 ◽  
pp. 134-148
Author(s):  
Vinod Kumar Kanvaria
Keyword(s):  
Teaching And Learning ◽  
Meaning Making ◽  
Life Experiences ◽  
Optimum Level ◽  
Mathematical Meaning ◽  
Conceptual Semantics ◽  
Simple Event ◽  
Semantics And Pragmatics ◽  
Contextual Values ◽  
Mathematical Semantics

The current chapter throws light on mathematical semantics and pragmatics. Believing that the mathematics has its own language and hence linguistics principles, the chapter tries to have an in-depth insight on how learner makes a meaning from an even simple event, while it takes place, and how these finally are assimilated by the learner. As learning is also experiential in nature, the contextual values, relationship, rapport, trust, confidence, in addition to simple interaction and plain interaction between learners and facilitators, play a vital and significant role in conceptual semantics and pragmatics of events and understanding of underlying mathematics. Context and situation are capable enough of changing perception-based mathematical meaning and meaning-making process, based on linguistics, associated with even the similar simple events. Hence, the context and situations must be created, associated and exploited up to the optimum level for enhanced conceptual teaching and learning of mathematics at par the daily life experiences for a better meaning-making process.

scholarly journals Implementing QVT-R via semantic interpretation in UML-RSDS

2020 ◽  
Author(s):  
K. Lano ◽  
S. Kolahdouz-Rahimi
Keyword(s):  
Model Transformation ◽  
Semantic Interpretation ◽  
Model Transformations ◽  
Tool Support ◽  
Transformation Language ◽  
Efficient Code ◽  
Model Transformation Language ◽  
Multiple Languages ◽  
Mathematical Semantics ◽  
Qvt Relations

Abstract The QVT-Relations (QVT-R) model transformation language is an OMG standard notation for model transformation specification. It is highly declarative and supports (in principle) bidirectional (bx) transformation specification. However, there are many unclear or unsatisfactory aspects to its semantics, which is not precisely defined in the standard. UML-RSDS is an executable subset of UML and OCL. It has a precise mathematical semantics and criteria for ensuring correctness of applications (including model transformations) by construction. There is extensive tool support for verification and for production of 3GL code in multiple languages (Java, C#, C++, C, Swift and Python). In this paper, we define a translation from QVT-R into UML-RSDS, which provides a logically oriented semantics for QVT-R, aligned with the RelToCore mapping semantics in the QVT standard. The translation includes variation points to enable specialised semantics to be selected in particular transformation cases. The translation provides a basis for verification and static analysis of QVT-R specifications and also enables the production of efficient code implementations of QVT-R specifications. We evaluate the approach by applying it to solve benchmark examples of bx.

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