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You know, discussion of relational logic
thus far, we have assumed that there is a

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one to one relationship between ground
terms in our language and objects in the

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application area we're trying to describe
For example, we have been assuming a

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unique name for each person. In
Arithmetic, we've been assuming unique

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term for each number. This is often called
Isomorphic Representation because if the

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1-to-1 relationship between ground terms
and objects in the world. This approach

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makes things conceptually simple and it's
a reasonably way to go in many

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circumstances but not always. In natural
language for example, we often find it

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convenient to use more than one term to
refer to the same real world object. For

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example, we sometimes have multiple names
for the same person, Michael and Mike And

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in elementary arithmetic, we frequently
use different terms to refer to the same

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number, two + two, two  two, s of s of s
of s of zero and so forth. In Relational

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Logic, we can axiomatize this
coreferentiality of terms in the form or

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equations. An equation is where we are
stating that to possibly distinct terms,

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referred to the same word object For
example, to express the coreferentiality

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of f of (a) and f of (b), we write equal f
of (a), f of (b). We can also distinguish

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terms; distinguish terms by writing
negated equations. To say that two terms

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referred to different objects, we write
not equal f of (a), f of (b), for example.

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So, since the quality of such common
relation and what follows a right

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equations with the infix operator equal
sign. For example, writing f(a) = f(b) in

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place of equal f(a), f(b). However, this
is just syntactic sugar. We must remember

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that as far as our logic is concerned,
syntactically and semantically, an

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equation is just a relational sentence
involving a relation constant like any

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other. We start this lesson by
axiomatizing the equal relation as an

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ordinary binary relation. We then discuss
the substitution of equals for equals in

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other expressions. And finally, we talk
about how to expand our pre-syste m for

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[inaudible] about equality.