9.4 KiB
| title | TARGET DECK | FILE TAGS | tags | ||
|---|---|---|---|---|---|
| Propositional Logic | Obsidian::STEM | logic::0-order |
|
Overview
Propositional logic (or 0-order logic) refers to the manipulation of propositions using the following five logical operators: \neg, \land, \lor, \Rightarrow, \Leftrightarrow.
%%ANKI Basic Who is the author of "The Science of Programming"? Back: David Gries Reference: Gries, David. The Science of Programming. Texts and Monographs in Computer Science. New York: Springer-Verlag, 1981.
END%%
%%ANKI
Basic
What are the constant propositions?
Back: T and F
Reference: Gries, David. The Science of Programming. Texts and Monographs in Computer Science. New York: Springer-Verlag, 1981.
END%%
%%ANKI
Basic
What are the five propositional logical operators?
Back: \neg, \land, \lor, \Rightarrow, and \Leftrightarrow
Reference: Gries, David. The Science of Programming. Texts and Monographs in Computer Science. New York: Springer-Verlag, 1981.
END%%
%%ANKI
Cloze
Gries replaces logical operator {\Leftrightarrow} in favor of {=}.
Reference: Gries, David. The Science of Programming. Texts and Monographs in Computer Science. New York: Springer-Verlag, 1981.
END%%
%%ANKI
Basic
How does Lean define propositional equality?
Back: Expressions a and b are propositionally equal iff a = b is true.
Reference: Avigad, Jeremy. ‘Theorem Proving in Lean’, n.d.
Tags: lean
END%%
%%ANKI
Basic
How does Lean define propext?
Back:
axiom propext {a b : Prop} : (a ↔ b) → (a = b)
Reference: Avigad, Jeremy. ‘Theorem Proving in Lean’, n.d. Tags: lean
END%%
%%ANKI
Basic
What Lean theorem justifies Gries choice of = over \Leftrightarrow?
Back: propext
Reference: Gries, David. The Science of Programming. Texts and Monographs in Computer Science. New York: Springer-Verlag, 1981.
Tags: lean
END%%
%%ANKI
Basic
What name is given to \land operands?
Back: Conjuncts
Reference: Gries, David. The Science of Programming. Texts and Monographs in Computer Science. New York: Springer-Verlag, 1981.
END%%
%%ANKI
Basic
What name is given to \lor operands?
Back: Disjuncts
Reference: Gries, David. The Science of Programming. Texts and Monographs in Computer Science. New York: Springer-Verlag, 1981.
END%%
%%ANKI
Basic
What name is given to operand a in a \Rightarrow b?
Back: The antecedent
Reference: Gries, David. The Science of Programming. Texts and Monographs in Computer Science. New York: Springer-Verlag, 1981.
END%%
%%ANKI
Basic
What name is given to operand b in a \Rightarrow b?
Back: The consequent
Reference: Gries, David. The Science of Programming. Texts and Monographs in Computer Science. New York: Springer-Verlag, 1981.
END%%
%%ANKI Basic What does the evaluation model of propositional logic refer to? Back: An interpretation of propositional logic that associates values to identifiers. Reference: Gries, David. The Science of Programming. Texts and Monographs in Computer Science. New York: Springer-Verlag, 1981.
END%%
%%ANKI Basic Evaluation model. What is a state? Back: A function mapping identifiers to values. Reference: Gries, David. The Science of Programming. Texts and Monographs in Computer Science. New York: Springer-Verlag, 1981.
END%%
%%ANKI Basic What is necessary to determine if a proposition is well-defined? Back: A state to evaluate against. Reference: Gries, David. The Science of Programming. Texts and Monographs in Computer Science. New York: Springer-Verlag, 1981.
END%%
%%ANKI
Basic
Is (b \land c) well-defined in \{(b, T), (c, F)\}?
Back: Yes
Reference: Gries, David. The Science of Programming. Texts and Monographs in Computer Science. New York: Springer-Verlag, 1981.
END%%
%%ANKI
Basic
Is (b \lor d) well-defined in \{(b, T), (c, F)\}?
Back: No
Reference: Gries, David. The Science of Programming. Texts and Monographs in Computer Science. New York: Springer-Verlag, 1981.
END%%
%%ANKI Basic Evaluation model. What does it mean for a proposition to be a tautology? Back: A proposition is true in every state it is well-defined in. Reference: Gries, David. The Science of Programming. Texts and Monographs in Computer Science. New York: Springer-Verlag, 1981.
END%%
%%ANKI
Basic
What C operator corresponds to \neg?
Back: !
Reference: Gries, David. The Science of Programming. Texts and Monographs in Computer Science. New York: Springer-Verlag, 1981.
Tags: c
END%%
%%ANKI
Basic
What C operator corresponds to \land?
Back: There isn't one.
Reference: Gries, David. The Science of Programming. Texts and Monographs in Computer Science. New York: Springer-Verlag, 1981.
Tags: c
END%%
%%ANKI
Basic
What C operator corresponds to \lor?
Back: There isn't one.
Reference: Gries, David. The Science of Programming. Texts and Monographs in Computer Science. New York: Springer-Verlag, 1981.
Tags: c
END%%
%%ANKI
Basic
What C operator corresponds to \Rightarrow?
Back: There isn't one.
Reference: Gries, David. The Science of Programming. Texts and Monographs in Computer Science. New York: Springer-Verlag, 1981.
Tags: c
END%%
%%ANKI
Basic
What C operator corresponds to \Leftrightarrow?
Back: =
Reference: Gries, David. The Science of Programming. Texts and Monographs in Computer Science. New York: Springer-Verlag, 1981.
Tags: c
END%%
%%ANKI Basic Evaluation model. What does a proposition represent? Back: The set of states in which it is true. Reference: Gries, David. The Science of Programming. Texts and Monographs in Computer Science. New York: Springer-Verlag, 1981.
END%%
%%ANKI
Basic
Evaluation model. What proposition represents states \{(b, T)\} and \{(c, F)\}?
Back: b \lor \neg c
Reference: Gries, David. The Science of Programming. Texts and Monographs in Computer Science. New York: Springer-Verlag, 1981.
END%%
%%ANKI
Basic
Evaluation model. What set of states does a \land b represent?
Back: The set containing just state \{(a, T), (b, T)\}.
Reference: Gries, David. The Science of Programming. Texts and Monographs in Computer Science. New York: Springer-Verlag, 1981.
END%%
%%ANKI
Basic
Evaluation model. What is sloppy about phrase "the states in b \lor \neg c"?
Back: b \lor \neg c is not a set.
Reference: Gries, David. The Science of Programming. Texts and Monographs in Computer Science. New York: Springer-Verlag, 1981.
END%%
%%ANKI
Basic
When is p stronger than q?
Back: When p \Rightarrow q.
Reference: Gries, David. The Science of Programming. Texts and Monographs in Computer Science. New York: Springer-Verlag, 1981.
END%%
%%ANKI
Basic
When is p weaker than q?
Back: When q \Rightarrow p.
Reference: Gries, David. The Science of Programming. Texts and Monographs in Computer Science. New York: Springer-Verlag, 1981.
END%%
%%ANKI
Basic
What is the weakest proposition?
Back: T
Reference: Gries, David. The Science of Programming. Texts and Monographs in Computer Science. New York: Springer-Verlag, 1981.
END%%
%%ANKI
Basic
What set of states does T represent?
Back: The set of all states.
Reference: Gries, David. The Science of Programming. Texts and Monographs in Computer Science. New York: Springer-Verlag, 1981.
END%%
%%ANKI
Basic
What is the strongest proposition?
Back: F
Reference: Gries, David. The Science of Programming. Texts and Monographs in Computer Science. New York: Springer-Verlag, 1981.
END%%
%%ANKI
Basic
What set of states does F represent?
Back: The set of no states.
Reference: Gries, David. The Science of Programming. Texts and Monographs in Computer Science. New York: Springer-Verlag, 1981.
END%%
%%ANKI
Basic
Evaluation model. Why is b \land c stronger than b \lor c?
Back: The former represents a subset of the states the latter represents.
Reference: Gries, David. The Science of Programming. Texts and Monographs in Computer Science. New York: Springer-Verlag, 1981.
END%%
%%ANKI
Basic
How is \Rightarrow written in terms of other logical operators?
Back: p \Rightarrow q is equivalent to \neg p \lor q.
Reference: Gries, David. The Science of Programming. Texts and Monographs in Computer Science. New York: Springer-Verlag, 1981.
END%%
%%ANKI
Basic
How is \Leftrightarrow written in terms of other logical operators?
Back: p \Leftrightarrow q is equivalent to (p \Rightarrow q) \land (q \Rightarrow p).
Reference: Gries, David. The Science of Programming. Texts and Monographs in Computer Science. New York: Springer-Verlag, 1981.
END%%
References
- Avigad, Jeremy. ‘Theorem Proving in Lean’, n.d.
- Gries, David. The Science of Programming. Texts and Monographs in Computer Science. New York: Springer-Verlag, 1981.