scholarly journals The algebra of recursive graph transformation language UnCAL: complete axiomatisation and iteration categorical semantics

2016 ◽  
Vol 28 (2) ◽  
pp. 287-337 ◽  
Author(s):  
MAKOTO HAMANA ◽  
KAZUTAKA MATSUDA ◽  
KAZUYUKI ASADA
Keyword(s):  
Functional Programming ◽  
Query Language ◽  
Graph Transformation ◽  
General Interest ◽  
Transformation Language ◽  
Interesting Connection ◽  
Database Query Language ◽  
Mathematical Foundations ◽  
Lazy Functional Programming ◽  
Categorical Semantics

The aim of this paper is to provide mathematical foundations of a graph transformation language, called UnCAL, using categorical semantics of type theory and fixed points. About 20 years ago, Bunemanet al. developed a graph database query language UnQL on the top of a functional meta-language UnCAL for describing and manipulating graphs. Recently, the functional programming community has shown renewed interest in UnCAL, because it provides an efficient graph transformation language which is useful for various applications, such as bidirectional computation.In order to make UnCAL more flexible and fruitful for further extensions and applications, in this paper, we give a more conceptual understanding of UnCAL using categorical semantics. Our general interest of this paper is to clarify what is the algebra of UnCAL. Thus, we give an equational axiomatisation and categorical semantics of UnCAL, both of which are new. We show that the axiomatisation is complete for the original bisimulation semantics of UnCAL. Moreover, we provide a clean characterisation of the computation mechanism of UnCAL called ‘structural recursion on graphs’ using our categorical semantics. We show a concrete model of UnCAL given by the λG-calculus, which shows an interesting connection to lazy functional programming.

scholarly journals Does Justification Aim at Truth?

2011 ◽  
Vol 41 (1) ◽  
pp. 51-71 ◽  
Author(s):  
Peter J. Graham
Keyword(s):  
Crucial Role ◽  
Epistemic Justification ◽  
General Interest ◽  
Common View ◽  
Interesting Part ◽  
Interesting Connection ◽  
Epistemic Externalism

Does epistemic justification aim at truth? The vast majority of epistemologists instinctively answer ‘Yes’; it's the textbook response. Joseph Cruz and John Pollock surprisingly say no. In ‘The Chimerical Appeal of Epistemic Externalism’ they argue that justification bears no interesting connection to truth; justification does not even aim at truth. ‘Truth is not a very interesting part of our best understanding’ of justification (C&P 2004, 137); it has no ‘connection to the truth.’ A ‘truth-aimed … epistemology is not entitled to carry the day’ (C&P 2004, 138, emphasis added).Pollock and Cruz's argument for this surprising conclusion is of general interest for it is ‘out of step with a very common view on the part of epistemologists, both internalist and externalist alike’ (C&P 2004, 136), as nearly all ‘epistemologists have claimed that truth and falsity play a crucial role in distinguishing between justified and unjustified beliefs [for] believing truths is the ultimate aim of human rational cognition’ (C&P 2004, 125; cf. Audi 1988).

Keyword-Based Language for Mobile Phones Query Services

2007 ◽  
pp. 369-374
Author(s):  
Z. Abdul-Mehdi
Keyword(s):  
Mobile Phones ◽  
Query Language ◽  
Development Work ◽  
Database Query ◽  
Work Related ◽  
Database Query Language ◽  
Query System

This article will highlight the framework opted by the authors in developing a database query system for usage on mobile phones. As the development work is still in progress, the authors will share some of the approaches taken in developing a prototype for a relationally complete database query language. This work concentrates on developing an application-independent, relationally complete database query language. The remainder of this article is organized as follows. The next section presents some of the existing work related to the study. We then introduce and describe the framework undertaken in order to develop a database query system for mobile phones, and discuss the prototype of the database query language used by the system. We end with our conclusion.

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