Introduction - Charles Ling
... Example: {R, ~P, ~ Q} Example: {~ P, ~ Q, ~ R} Example: P Non-Example: {Q, R, ~ P} NB: Every Horn clause can be written as a “rule”. {~ P, ~ Q, R} ...
... Example: {R, ~P, ~ Q} Example: {~ P, ~ Q, ~ R} Example: P Non-Example: {Q, R, ~ P} NB: Every Horn clause can be written as a “rule”. {~ P, ~ Q, R} ...
Document
... Quantifiers and First Order Logic Formulas in Predicate Logic All statement formulas are considered formulas Each n, n =1,2,...,n-place predicate P( x1 , x2 , ... , xn ) containing the variables x1 , x2 , ... , xn is a formula. If A and B are formulas, then the expressions ~A, (A∧B), (A∨B) , A ...
... Quantifiers and First Order Logic Formulas in Predicate Logic All statement formulas are considered formulas Each n, n =1,2,...,n-place predicate P( x1 , x2 , ... , xn ) containing the variables x1 , x2 , ... , xn is a formula. If A and B are formulas, then the expressions ~A, (A∧B), (A∨B) , A ...
Propositional/First
... • A valid sentence is true in all worlds under all interpretations • If an implication sentence can be shown to be valid, then— given its premise—its consequent can be derived • Different logics make different commitments about what the world is made of and what kind of beliefs we can have • Proposi ...
... • A valid sentence is true in all worlds under all interpretations • If an implication sentence can be shown to be valid, then— given its premise—its consequent can be derived • Different logics make different commitments about what the world is made of and what kind of beliefs we can have • Proposi ...
Logic - Decision Procedures
... (3) I have not filed any of them that I can read; (4) None of them, that are written on one sheet, are undated; (5) All of them, that are not crossed, are in black ink; (6) All of them, written by Brown, begin with "Dear Sir"; (7) All of them, written on blue paper, are filed; (8) None of them, writ ...
... (3) I have not filed any of them that I can read; (4) None of them, that are written on one sheet, are undated; (5) All of them, that are not crossed, are in black ink; (6) All of them, written by Brown, begin with "Dear Sir"; (7) All of them, written on blue paper, are filed; (8) None of them, writ ...
Notes on Propositional and Predicate Logic
... • Simplify all subexpressions of the form (not (not p)) to p • Move all occurrences of or “inside” occurrences of and • Simplify all or- expressions for example by rewriting (or (or p q) r) as (or p q r) , and similarly for and Each premise is converted to conjunctive normal form in this way. Then t ...
... • Simplify all subexpressions of the form (not (not p)) to p • Move all occurrences of or “inside” occurrences of and • Simplify all or- expressions for example by rewriting (or (or p q) r) as (or p q r) , and similarly for and Each premise is converted to conjunctive normal form in this way. Then t ...
Natural deduction for predicate logic
... This suggests that to prove a formula of the form ∀xφ, we can prove φ with some arbitrary but fresh variable x0 substituted for x. That is, we want to prove the formula φ[x0 /x]. On the previous slide, we used n as a fresh variable, but in our formal proofs, we adopt the convention of using subscri ...
... This suggests that to prove a formula of the form ∀xφ, we can prove φ with some arbitrary but fresh variable x0 substituted for x. That is, we want to prove the formula φ[x0 /x]. On the previous slide, we used n as a fresh variable, but in our formal proofs, we adopt the convention of using subscri ...
Chapter 5: Methods of Proof for Boolean Logic
... TT-contradictory. This will require some extra footwork in cases in which we have other kinds of contradictions. § 5.4 Arguments with inconsistent premises If a set of premises is inconsistent, any argument having those premises is valid. (If the premises are inconsistent, there is no possible circu ...
... TT-contradictory. This will require some extra footwork in cases in which we have other kinds of contradictions. § 5.4 Arguments with inconsistent premises If a set of premises is inconsistent, any argument having those premises is valid. (If the premises are inconsistent, there is no possible circu ...
Predicate Logic - Teaching-WIKI
... Anyone standing in the rain will get wet. and then use this knowledge. For example, suppose we also learn that Jan is standing in the rain. • We'd like to conclude that Jan will get wet. But each of these sentences would just be a represented by some proposition, say P, Q and R. What relationship is ...
... Anyone standing in the rain will get wet. and then use this knowledge. For example, suppose we also learn that Jan is standing in the rain. • We'd like to conclude that Jan will get wet. But each of these sentences would just be a represented by some proposition, say P, Q and R. What relationship is ...
The Foundations: Logic and Proofs
... raining.” then p →q denotes “If I am at home then it is raining.” In p →q , p is the hypothesis (antecedent or premise) and q is the conclusion (or consequence). ...
... raining.” then p →q denotes “If I am at home then it is raining.” In p →q , p is the hypothesis (antecedent or premise) and q is the conclusion (or consequence). ...
Lecture 3
... • “If you clean the car then you can go out” • Could we infer either of the following? – “if you don't clean the car then you can't go out” or – “if you were allowed out, then you must have cleaned the car”. ...
... • “If you clean the car then you can go out” • Could we infer either of the following? – “if you don't clean the car then you can't go out” or – “if you were allowed out, then you must have cleaned the car”. ...
