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| title | TARGET DECK | FILE TAGS | tags | ||
|---|---|---|---|---|---|
| Predicate Logic | Obsidian::STEM | logic::predicate |
|
Overview
A branch of logic that uses quantified variables over non-logical objects. A predicate is a sentence with some number of free variables. A predicate with free variables "plugged in" is a prop-logic.
%%ANKI Cloze {Predicate} logic is also known as {first}-order logic. Reference: Oscar Levin, Discrete Mathematics: An Open Introduction, 3rd ed., n.d., https://discrete.openmathbooks.org/pdfs/dmoi3-tablet.pdf.
END%%
%%ANKI Basic What is a predicate? Back: A sentence with some number of free variables. Reference: Oscar Levin, Discrete Mathematics: An Open Introduction, 3rd ed., n.d., https://discrete.openmathbooks.org/pdfs/dmoi3-tablet.pdf.
END%%
%%ANKI Basic What distinguishes a predicate from a proposition? Back: A proposition does not contain free variables. Reference: Oscar Levin, Discrete Mathematics: An Open Introduction, 3rd ed., n.d., https://discrete.openmathbooks.org/pdfs/dmoi3-tablet.pdf.
END%%
%%ANKI
Basic
How are propositions defined in terms of predicates?
Back: A proposition is a predicate with 0 free variables.
Reference: Oscar Levin, Discrete Mathematics: An Open Introduction, 3rd ed., n.d., https://discrete.openmathbooks.org/pdfs/dmoi3-tablet.pdf.
END%%
%%ANKI
Basic
Why is "3 + x = 12" not a proposition?
Back: Because x is a variable.
Reference: Oscar Levin, Discrete Mathematics: An Open Introduction, 3rd ed., n.d., https://discrete.openmathbooks.org/pdfs/dmoi3-tablet.pdf.
END%%
Sets
A state is a function that maps identifiers to values. A predicate can be equivalently seen as a representation of the set of states in which it is true.
%%ANKI
Basic
Is (i \geq 0) well-defined in \{(i, -10)\}?
Back: Yes.
Reference: Gries, David. The Science of Programming. Texts and Monographs in Computer Science. New York: Springer-Verlag, 1981.
END%%
%%ANKI
Basic
Is (i \geq 0) well-defined in \{(j, -10)\}?
Back: No.
Reference: Gries, David. The Science of Programming. Texts and Monographs in Computer Science. New York: Springer-Verlag, 1981.
END%%
%%ANKI
Basic
What predicate represents states \{(i, 0), (i, 2), (i, 4), \ldots\}?
Back: i \geq 0 is even.
Reference: Gries, David. The Science of Programming. Texts and Monographs in Computer Science. New York: Springer-Verlag, 1981.
END%%
%%ANKI
Basic
What is sloppy about phrase "the states in i + j = 0"?
Back: i + j = 0 is not a set but a representation of a set (of states).
Reference: Gries, David. The Science of Programming. Texts and Monographs in Computer Science. New York: Springer-Verlag, 1981.
END%%
Bibliography
- Gries, David. The Science of Programming. Texts and Monographs in Computer Science. New York: Springer-Verlag, 1981.
- Oscar Levin, Discrete Mathematics: An Open Introduction, 3rd ed., n.d., https://discrete.openmathbooks.org/pdfs/dmoi3-tablet.pdf.