On the mathematical synthesis of equational logics

@article{Fiore2011OnTM,
  title={On the mathematical synthesis of equational logics},
  author={Marcelo P. Fiore and Chung-Kil Hur},
  journal={Log. Methods Comput. Sci.},
  year={2011},
  volume={7}
}
  • M. FioreC. Hur
  • Published 15 July 2011
  • Mathematics
  • Log. Methods Comput. Sci.
We provide a mathematical theory and methodology for synthesising equational logics from algebraic metatheories. We illustrate our methodology by means of two applications: a rational reconstruction of Birkhoff's Equational Logic and a new equational logic for reasoning about algebraic structure with name-binding operators. 

AN EQUATIONAL METALOGIC FOR MONADIC EQUATIONAL SYSTEMS

The paper presents algebraic and logical developments. From the algebraic viewpoint, we introduce Monadic Equational Systems as an abstract enriched notion of equational presentation. From the

I Current Research Groups 19 Iv Details 113

  • Computer Science
The MPI-SWS review period covers the period May 2011 – October 2013 and presents a general overview of the goals, structure, and organization of the institute, not specific to the present review period.

References

SHOWING 1-10 OF 24 REFERENCES

Term Equational Systems and Logics: (Extended Abstract)

Nominal Equational Logic

Second-Order Equational Logic (Extended Abstract)

We extend universal algebra and its equational logic from first to second order as follows.

On the Structure of Abstract Algebras

  • G. BirkhoffP. Hall
  • Mathematics
    Mathematical Proceedings of the Cambridge Philosophical Society
  • 1935
The following paper is a study of abstract algebras qua abstract algebras. As no vocabulary suitable for this purpose is current, I have been forced to use a number of new terms, and extend the

Second-Order and Dependently-Sorted Abstract Syntax

  • M. Fiore
  • Computer Science
    2008 23rd Annual IEEE Symposium on Logic in Computer Science
  • 2008
The paper develops a mathematical theory in the spirit of categorical algebra that provides a model theory for second-order and dependently-sorted syntax. The theory embodies notions such as

On the construction of free algebras for equational systems

Second-Order Algebraic Theories - (Extended Abstract)

The paper introduces the notion of second-order algebraic theory and develops its basic theory and gives the first formalisation of notions such as encodings and transforms in the context of languages with variable binding.

Second-order equational logic

We extend universal algebra and its equational logic from first to second order as follows. 1. We consider second-order equational presentations as specified by identities between second-order terms,

A New Approach to Abstract Syntax with Variable Binding

Inductively defined FM-sets involving the name-abstraction set former can correctly encode syntax modulo renaming of bound variables, and the standard theory of algebraic data types can be extended to encompass signatures involving binding operators.

FUNCTORIAL SEMANTICS OF ALGEBRAIC THEORIES.

  • F. W. Lawvere
  • Mathematics
    Proceedings of the National Academy of Sciences of the United States of America
  • 1963
Equi-inclination Weissenberg photographs were taken about the a axis with filtered CuKa radiation, using the multiple film technique, and a total of 2,511 reflections were indexed, of which 2,015 were nonzero, representing about 90 per cent of the data accessible in the copper sphere.