Unformatted text preview: is a snurd.” Solution: ¬∃x S(x) What is this equivalent to? Solution: ∀x ¬ S(x) Transla$on (cont) ༉ U = {ﬂeegles, snurds, thingamabobs} F(x): x is a ﬂeegle S(x): x is a snurd T(x): x is a thingamabob “All ﬂeegles are snurds.” Solution: ∀x (F(x)→ S(x)) Transla$on (cont) ༉ U = {ﬂeegles, snurds, thingamabobs} F(x): x is a ﬂeegle S(x): x is a snurd T(x): x is a thingamabob “Some ﬂeegles are thingamabobs.” Solution: ∃x (F(x) ∧ T(x)) Transla$on (cont) ༉ U = {ﬂeegles, snurds, thingamabobs} F(x): x is a ﬂeegle S(x): x is a snurd T(x): x is a thingamabob “No snurd is a thingamabob.” ¬ “Some snurd is a thingamabob.” Solution: ¬∃x (S(x) ∧ T(x)) Solution: ∀x (¬S(x) ∨ ¬T(x)) Transla$on (cont) ༉ U = {ﬂeegles, snurds, thingamabobs} F(x): x is a ﬂeegle S(x): x is a snurd T(x): x is a thingamabob “If any ﬂeegle is a snurd then it is also a thingamabob.” Solution: ∀x ((F(x) ∧ S(x)) → T(x)) System Speciﬁca$on Example ༉ For example, translate into predicate logic: ༉ “Every mail message larger than one megabyte will be compressed.” ༉ “If a user is active, then at least one network link will be available.” ༉ Decide on predicates and domains for the variables: ༉ Let L(m, y) be “Mail message m is larger than y megabytes.” ༉ Let C(m) denote “Mail message m will be compressed.” ༉ Let A(u) represent “User u is active.” ༉ Let S(n, x) represent “Network link n is state x.” ༉ No...
View
Full Document
 Spring '14
 M.Nojoumian
 Computer Science, Logic, ∀x, Quan

Click to edit the document details