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In predicate logic, you are able to use either a single capital letter (R) for a sentence like "It is raining" or a letter followed by a small letter (Ra) which represents an atomic sentence.

In an atomic sentence in logic, there's one subject and a verb which is similar to the definition of a simple sentence in English language which also has a subject and a verb.

So, what does a simple sentence mean in logic if the atomic sentence is already the one with a subject and a verb?

Here's a quote from the text I was reading:

Simple Sentences: upper case letters
English: “It is raining”
Predicate Logic: “R”

Atomic Sentences: an n-place predicate letter followed by n lower case letters.
English: “Mary is tall”
Predicate Logic: “Tm”

What are some other examples of sentences represented by a single capital letter besides "It is raining" denoted by 'R'? If I am guessing correctly they should begin with a pronoun similar to "It" and "they" etc.

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The more conventional notation for Tm in you text would be T(m) with m being an individual constant denoting Mary, and T(x) being a 1-place predicate "x is tall". One can also get atomic sentences from many place predicates with multiple constants in them, e.g. L(m,n) for "Mary loves Nick". These are the typical atomic sentences of predicate calculus. Finally, there are 0-place predicates (propositions) that require no constants at all, like R for "it's raining". Your text calls them "simple sentences" if they do not decompose into smaller parts joined by connectives, etc. Such propositional constants are most common in propositional calculus, a more elementary segment of predicate calculus.

The term "simple sentence" (no subordinate clauses) is also used in grammar, and does typically involve "subject" (typically noun or pronoun phrase) and "predicate" (typically verb phrase). In case of atomic sentences based on 1-place predicates we have an individual constant and a predicate, so there is a clear parallelism between grammar and logic. Many place predicates can be expressed using objects, adpositional phrases, etc. Since English grammar requires a subject in a sentence the placeholder pronoun "it" is often used fulfill this role when dealing with 0-place predicates.

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  • What are some other examples of simple sentences besides "It is raining" in predicate logic? – cpx Oct 14 '15 at 10:08

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