Introduction to Mathematical Linguistics |
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Page 33
... Example 2-1 : Simplify ~ p V ( p ^ q ) . 1. ~ p v ( p ^ q ) 2. ( ~ p v p ) ^ ( ~ p V q ) 3. ( p V ~ p ) ^ ( ~ p V q ) 4. Tλ ( ~ p v q ) 5. ( ~ p v q ) ^ T 6. ~ pvq Distr . Comm . Compl . Comm . Ident . Because all the lines are ...
... Example 2-1 : Simplify ~ p V ( p ^ q ) . 1. ~ p v ( p ^ q ) 2. ( ~ p v p ) ^ ( ~ p V q ) 3. ( p V ~ p ) ^ ( ~ p V q ) 4. Tλ ( ~ p v q ) 5. ( ~ p v q ) ^ T 6. ~ pvq Distr . Comm . Compl . Comm . Ident . Because all the lines are ...
Page 62
... example . The truth value of the proposition H ( s ) depends on the nature of the predicate denoted by H and on the particular individual denoted by s . If H is ' is human ' and s is ' Socrates , ' then H ( s ) is true ; but if H is ...
... example . The truth value of the proposition H ( s ) depends on the nature of the predicate denoted by H and on the particular individual denoted by s . If H is ' is human ' and s is ' Socrates , ' then H ( s ) is true ; but if H is ...
Page 152
... examples of mathematical operations . In each of these instances we can think of the operation as converting one or a pair of things of the appropriate sort into another thing of the same kind . For example , the union of two sets is a ...
... examples of mathematical operations . In each of these instances we can think of the operation as converting one or a pair of things of the appropriate sort into another thing of the same kind . For example , the union of two sets is a ...
Contents
Infinite Sets | 4 |
The Predicate Calculus | 51 |
Further Aspects of Set Theory | 81 |
Copyright | |
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Common terms and phrases
alphabet argument form automaton axiom axiomatic system Chomsky computation conditional proof configuration connex constituent-structure contains context-free defined denoted derivation deterministic domain of discourse dominates elementary propositions equivalence classes equivalence relation example expression f f f f t f false finite number finite set G₁ given grammar G identity element infinite set input string input tape instantiation inverse irreflexive isomorphism logically equivalent mathematical monoid natural language negation node labeled nondeterministic notation null set occurrences one-to-one correspondence operation ordered pairs ordered triples partially ordered set partition positive integers precedes predicate premises properties propositional function prove pushdown quantifier R₁ recursive definition reflexive regular sets rules S₁ sentence sequence specified symmetric tautology terminal string terminal symbols theorem transformational grammar transitive tree true truth table truth value Turing machine two-sided identity type 3 grammar type 3 languages V₁ V₂ valid variable Venn diagram