On the mathematical synthesis of equational logics

  title={On the mathematical synthesis of equational logics},
  author={Marcelo P. Fiore and Chung-Kil Hur},
  journal={Log. Methods Comput. Sci.},
  • 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. 


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.



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.


  • 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.