CL/CL*
The alphabet for CL
What is P and Q
What are the operators for TFL and their names, and English translation:
&: Conjunction, and
→: conditional, then
o: disjunction, or
↔: biconditional, iff
~: negation, not
What does it mean to create an extensional model?
and What does it mean to create a total, partial, and adequate model?
Extensional: Formal, contains the domain, all extensions, and all referents.
Total, partial, and adequate model: contains only the truth values asked, domain is not needed
You can eat sugary cereal (c) for breakfast then you cannot eat a pop tart (a) for lunch
(Bc→~Ba)
Is this in disjunctive normal form?
(Gd & Fd & ∼H f)
Nope
The operators in CL*
What is a conditional
What is the truth table for conjunction and disjunction
Disjunction: TTTF
What is the difference between a term function and a predicate function?
Term function: points to the name of each individual, represented by tau
Predicate function: points to each predicate to the set of individuals that include the predicate, represented by a pi
Create a truth table of the wff:
~ ( Ab & Gb ) → Fh )
Only One True in the second row
Is this in disjunctive form?
(Fa & Gb) ◦ (Fa & Gb)
Yessir
How do you make this an assertion?
Go pet the Cat!
What is I love petting the cat?
(Numerous answers)
What is the main connective in this wff?
~(Fa o (Ab&Jb))
What is ~
Create an extensional, partial, and adequate model for this wff:
((Fa→Ga)→Ga)
Must include domain, terms, and predicates
Satisfiable,
Contingent,
Valid
Check to see if the following wff is satisfiable
{Ha, (Id → ∼Ha), Id}
Not satisfiable
What is the antecedent and consequent?
(P →(P →P)
What is antecedent P
What is the consequent P →P
Logical falsity: cannot ever be true
Logical truth: cannot ever be false
Logical contingency: truth values are both true and false
Create an extensional, partial, adequate model that makes this wff false:
((Fa→Gb) o (~Fb&Ga)
Answers Vary
Create a combined truth table:
(Ab&Fc),(AboFc), ~Fc
TFFF
TTTF
FTFT
Make a combined truth table to see if the wff is valid:
{(Fa → Gb), (Gb → Hc)} |= (Fa → Hc)
Valid!
What are the subformulas in this wff?
((( P →P) →Q) →Q)
What are: (P→P)
(P→P)→Q)
Explain the differences between logical satisfiability, entailment, and validity.
Satisfiable: an entire row is true
Entailment: every row where P is true, Q is false as well
Validity: It is impossible for the premise to be true and the conclusion false
Create an extensional, partial, adequate model with a true wff
Answers vary
Create a combined truth table and label the semantic properties:
TTFFTTT
TTFTTTFT
TFFFTFFF
Satisfiable, contingent, entails
Convert the following to disjunctive normal form
(Gd ↔ ∼H f)
(Gd&~Af) o (~Gd&Af)