Handout 2 - The Logic Manual
... The argument with all sentences in Γ as premisses and φ as conclusion is valid if and only if there is no L1 -structure under which: (i) all sentences in Γ are true; and (ii) φ is false. Notation: when this argument is valid we write Γ φ. {P → ¬Q, Q} |= ¬P means that the argument whose premises ar ...
... The argument with all sentences in Γ as premisses and φ as conclusion is valid if and only if there is no L1 -structure under which: (i) all sentences in Γ are true; and (ii) φ is false. Notation: when this argument is valid we write Γ φ. {P → ¬Q, Q} |= ¬P means that the argument whose premises ar ...
Mary fixed the chair with glue
... knowledge is inferred by inference rules such as modus ponens or resolution. If the computer can find a path from given facts to a new theorem, the path corresponds to a proof and finding such a path constitutes an example of artificial intelligence ...
... knowledge is inferred by inference rules such as modus ponens or resolution. If the computer can find a path from given facts to a new theorem, the path corresponds to a proof and finding such a path constitutes an example of artificial intelligence ...
Heuristic Search - Dr. Sadi Evren SEKER
... Let f=~(x+ ~y(~x+z)). (a) Write out the truth table for f. (b) Convert the truth table to CNF. (c) Show the series of steps DPLL makes while solving the resulting formula. Assume variables chosen for splitting in the order x, y, z. Using the same f from the first part, follow the 3-CNF conversion al ...
... Let f=~(x+ ~y(~x+z)). (a) Write out the truth table for f. (b) Convert the truth table to CNF. (c) Show the series of steps DPLL makes while solving the resulting formula. Assume variables chosen for splitting in the order x, y, z. Using the same f from the first part, follow the 3-CNF conversion al ...
slides - Department of Computer Science
... Theorem (and Witnessing Theorem) out some axioms to get a universal theory that is a we need: conservative extension of TC 1. TC is universal theory 2. Make sure all terms in language describe functions from C; 3. We can assume We add function symbols (with defining axioms) in C. And the C-closure o ...
... Theorem (and Witnessing Theorem) out some axioms to get a universal theory that is a we need: conservative extension of TC 1. TC is universal theory 2. Make sure all terms in language describe functions from C; 3. We can assume We add function symbols (with defining axioms) in C. And the C-closure o ...
Lecture 2a: First-order Logic over words Formal Semantics for FO(<)
... u, [x 7→ i] |= ϕ1 ∨ ϕ2 iff u, [x 7→ i] |= ϕ1 or u, [x 7→ i] |= ϕ2 and by induction hypothesis, u, [x 7→ i] |= ϕk iff v, [x 7→ j] |= ϕk for k ∈ 1, 2. The result follows. Case 4: ϕ = ∃x. ψ If u, [x 7→ i] |= ∃x. ψ then there is a position i0 in u such that u, [x 7→ i0 ] |= ψ. Further since u ≡α v, ther ...
... u, [x 7→ i] |= ϕ1 ∨ ϕ2 iff u, [x 7→ i] |= ϕ1 or u, [x 7→ i] |= ϕ2 and by induction hypothesis, u, [x 7→ i] |= ϕk iff v, [x 7→ j] |= ϕk for k ∈ 1, 2. The result follows. Case 4: ϕ = ∃x. ψ If u, [x 7→ i] |= ∃x. ψ then there is a position i0 in u such that u, [x 7→ i0 ] |= ψ. Further since u ≡α v, ther ...
