Logic as a Tool 3mm Chapter 2: Deductive Reasoning in
... Alternatively, after finitely many applications of the Propositional Resolution rule, no new applications of the rule remain possible. If the empty clause is not derived by then, it cannot be derived at all, and hence the A1 , . . . , An and ¬B can be satisfied together, so the logical consequence A ...
... Alternatively, after finitely many applications of the Propositional Resolution rule, no new applications of the rule remain possible. If the empty clause is not derived by then, it cannot be derived at all, and hence the A1 , . . . , An and ¬B can be satisfied together, so the logical consequence A ...
PDF
... variant form of a deductive system. Like a deductive system, a Gentzen system has axioms and inference rules. But, unlike a deductive system, the basic building blocks in a Gentzen system are expressions called sequents, not formulas. More precisely, given a language L of well-formed formulas, a ded ...
... variant form of a deductive system. Like a deductive system, a Gentzen system has axioms and inference rules. But, unlike a deductive system, the basic building blocks in a Gentzen system are expressions called sequents, not formulas. More precisely, given a language L of well-formed formulas, a ded ...
Propositional Logic - faculty.cs.tamu.edu
... not interesting, since we would like everything to be consistent with the meaning of the connectives that we have just learned. For example, if the propositions a and b have been assigned the value t, then it is reasonable to insist that a ∧ b be assigned the value t as well. Therefore, we will intr ...
... not interesting, since we would like everything to be consistent with the meaning of the connectives that we have just learned. For example, if the propositions a and b have been assigned the value t, then it is reasonable to insist that a ∧ b be assigned the value t as well. Therefore, we will intr ...
L11
... because of the definition of . ● Since P Q R is false for 14 entries out of 16, we are left only with two entries to be tested for which is true. ...
... because of the definition of . ● Since P Q R is false for 14 entries out of 16, we are left only with two entries to be tested for which is true. ...
Discrete Structure
... i.e., If p is true, then q is true; but if p is not true, then q could be either true or false. E.g., let p = “You study hard.” q = “You will get a good grade.” p q = “If you study hard, then you will get a good grade.” (else, it could go either way) ...
... i.e., If p is true, then q is true; but if p is not true, then q could be either true or false. E.g., let p = “You study hard.” q = “You will get a good grade.” p q = “If you study hard, then you will get a good grade.” (else, it could go either way) ...
Logic and Proof - Collaboratory for Advanced Computing and
... Methods of Proving Theorems Proving implications p → q: Direct proof: Assume p is T, and use rules of inference to prove that q is T Indirect proof: Prove its contrapositive; assume ¬q, and prove ¬p Proof by cases: Prove (p1 ∨ p2) → q by proving (p1 → q) and (p1 → q) • Based on [(p1 ∨ p2) → q ...
... Methods of Proving Theorems Proving implications p → q: Direct proof: Assume p is T, and use rules of inference to prove that q is T Indirect proof: Prove its contrapositive; assume ¬q, and prove ¬p Proof by cases: Prove (p1 ∨ p2) → q by proving (p1 → q) and (p1 → q) • Based on [(p1 ∨ p2) → q ...
The Foundations: Logic and Proofs - UTH e
... Two compound propositions p and q are logically equivalent if p↔q is a tautology. We write this as p⇔q or as p≡q where p and q are compound propositions. Two compound propositions p and q are equivalent if and only if the columns in a truth table giving their truth values agree. This truth table sho ...
... Two compound propositions p and q are logically equivalent if p↔q is a tautology. We write this as p⇔q or as p≡q where p and q are compound propositions. Two compound propositions p and q are equivalent if and only if the columns in a truth table giving their truth values agree. This truth table sho ...
First order theories
... But there exists first order theories defined by axioms which are not sufficient for proving all T-valid formulas. ...
... But there exists first order theories defined by axioms which are not sufficient for proving all T-valid formulas. ...
slides - Department of Computer Science
... 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 of all functions is C itself. ...
... 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 of all functions is C itself. ...
study guide.
... • There are two main normal forms for the propositional formulas. One is called Conjunctive normal form (CNF) and is an ∧ of ∨ of either variables or their negations (here, by ∧ and ∨ we mean several formulas with ∧ between each pair, as in (¬x ∨ y ∨ z) ∧ (¬u ∨ y) ∧ x. A literal is a variable or its ...
... • There are two main normal forms for the propositional formulas. One is called Conjunctive normal form (CNF) and is an ∧ of ∨ of either variables or their negations (here, by ∧ and ∨ we mean several formulas with ∧ between each pair, as in (¬x ∨ y ∨ z) ∧ (¬u ∨ y) ∧ x. A literal is a variable or its ...
Logic I Fall 2009 Problem Set 5
... Logic I Fall 2009 Problem Set 5 In class I talked about SL being truth-functionally complete (TF-complete). For the problems below, use TLB’s definition of TF-completeness, according to which it is sets of connectives that are (or aren’t) TF-complete: Definition: A set of connectives is TF-complete if ...
... Logic I Fall 2009 Problem Set 5 In class I talked about SL being truth-functionally complete (TF-complete). For the problems below, use TLB’s definition of TF-completeness, according to which it is sets of connectives that are (or aren’t) TF-complete: Definition: A set of connectives is TF-complete if ...