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2. Goals. To learn about the notion of FO equivalenceFO EquivalenceEquivalent wffsSubstitution of equivalent wffsDeMorgan laws for quantifiersOther equivalence lawsTo learn about common FO equivalences and to gain skills in using them.. 3. Equivalence. Two sentences P and Q are equivalent" if
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1. 1 Formal Methods in Computer Science CS1502 FO Equivalence Patchrawat Uthaisombut
University of Pittsburgh
2. 2 Goals To learn about the notion of FO equivalence
FO Equivalence
Equivalent wffs
Substitution of equivalent wffs
DeMorgan laws for quantifiers
Other equivalence laws
To learn about common FO equivalences and to gain skills in using them.
3. 3 Equivalence Two sentences P and Q are equivalent if they have the same truth value in any circumstance.
P ? Q
4. 4 Equivalences Tautological equivalence: equivalent solely in virtue of the meaning of
the boolean connectives /\, \/, ~
FO equivalence: equivalent solely in virtue of the meaning of
the boolean connectives /\, \/, ~
the quantifiers ?, ?
the identity symbol =
5. 5 3 kinds of FO equivalences Tautological equivalence
Equivalence of wffs
Equivalence involving quantifiers
Use them with substitution law.
By classifying them, it should help use remember them better.
6. 6 Substitution Law Suppose S is a complete unit of something. Suppose P is a component of S. We write S as S(P) to emphasize that P is a component of S. If Q ? P, we can replace P in S(P) with Q. Equivalence depends on context. We get S(Q). Every other part of S is the same. S(P) ? S(Q).
