First-order equational
logic
Logic is the study of correct reasoning. It includes both formal and informal logic. Formal logic is the science of deductively valid inferences or of logical truths. It is a formal science investigating how conclusions follow from premises ...
consists of
quantifier-free terms of ordinary
first-order logic
First-order logic—also known as predicate logic, quantificational logic, and first-order predicate calculus—is a collection of formal systems used in mathematics, philosophy, linguistics, and computer science. First-order logic uses quantifie ...
, with equality as the only
predicate symbol In mathematical logic, a predicate variable is a predicate letter which functions as a "placeholder" for a relation (between terms), but which has not been specifically assigned any particular relation (or meaning). Common symbols for denoting predi ...
. The
model theory
In mathematical logic, model theory is the study of the relationship between formal theories (a collection of sentences in a formal language expressing statements about a mathematical structure), and their models (those structures in which the s ...
of this logic was developed into
universal algebra
Universal algebra (sometimes called general algebra) is the field of mathematics that studies algebraic structures themselves, not examples ("models") of algebraic structures.
For instance, rather than take particular groups as the object of study, ...
by
Birkhoff,
Grätzer
Grodziskie (; other names: Grätzer, Grodzisz) is a historical beer style from Poland made from oak-smoked wheat malt with a clear, light golden color, high carbonation, low alcohol content, low to moderate levels of hop bitterness, and a stro ...
, and
Cohn Cohn is a Jewish surname (related to the last name Cohen).
Notable people sharing the surname "Cohn"
* Al Cohn (1925–1988), American jazz saxophonist, arranger and composer
* Alan D. Cohn, American government official
* Alfred A. Cohn (1880†...
. It was later made into a branch of
category theory
Category theory is a general theory of mathematical structures and their relations that was introduced by Samuel Eilenberg and Saunders Mac Lane in the middle of the 20th century in their foundational work on algebraic topology. Nowadays, cate ...
by
Lawvere
Francis William Lawvere (; born February 9, 1937) is a mathematician known for his work in category theory, topos theory and the philosophy of mathematics.
Biography
Lawvere studied continuum mechanics as an undergraduate with Clifford Truesd ...
("algebraic theories").
[equational logic. (n.d.). The Free On-line Dictionary of Computing. Retrieved October 24, 2011, from Dictionary.com website: http://dictionary.reference.com/browse/equational+logic]
The terms of equational logic are built up from variables and constants using function symbols (or operations).
Syllogism
Here are the four
inference rule
In the philosophy of logic, a rule of inference, inference rule or transformation rule is a logical form consisting of a function which takes premises, analyzes their syntax, and returns a conclusion (or conclusions). For example, the rule of ...
s of logic.