Logic in Action

Meaning and Argument offers helpful procedures for symbolizing complex statements in Relational Predicate Logic (RPL) and RPL with identity (RPL=). Sentences with nested quantifiers and restricted relative clauses are very difficult to symbolize straight off, but these procedures make life that little bit easier.

Below are links to animated sequences that illustrate these procedures. The sentences begin in "hybrid matrix" form, with just the single main predicate, and the quantifiers arranged like singular terms. The quantifiers are then slid out into place, and the connectives and variables are added.

 

Sentences

All dogs bark
(See chapter 12; section 13.2)
An introductory sentence with a one-place predicate. The universal quantifier procedure is illustrated.

Someone works for Nadia
(See chapter 12; section 13.3)
A two-place predicate that makes use of the existential quantifier procedure.

Everyone loves someone
(See sections 13.1 - 13.4)
A two-place predicate and a nested quantifier, but straightforward sentence structure.

Some cup was put on every table by some man
(See sections 13.7 - 13.9)
A three place predicate with nested quantifiers in a complex order.

There's a time at which everyone eats every doughnut
(See sections 13.7 - 13.9)
Another three place predicate with nested quantifiers.

Only philosophers wear only diamonds
(See section 15.2)
Animated "only" strategies from 15.2. The first "only" has wide scope, the second one is nested, so both cases are covered.

Every cat that cleans himself cleans an animal that catches mice
(See sections 15.3)
Restrictive relative clauses with nested quantifiers.

If someone is tall, then he is bigger than Rachel
(see section 15.4)
A conditional with an existential in the antecedent, and an anaphoric pronoun in the consequent.

Every dog that has an owner obeys him
(see section 15.5)
An anaphoric pronoun whose anaphor is contained in the restrictive relative clause.

Some man who has a daughter wants her to attend Rutgers
(see section 15.5)
An anaphoric pronoun whose anaphor in contained in the restrictive relative clause that does not become a universal in the final statement.

The man Karen adores is friends with Bob
(see section 16.5)
A symbolization in RPL= involving "the".

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