deductive system
... A deductive system is a formal (mathematical) setup of reasoning. In order to describe a deductive system, a (formal) language system must first be in place, consisting of (well-formed) formulas, strings of symbols constructed according to some prescribed syntax. With the language in place, reasonin ...
... A deductive system is a formal (mathematical) setup of reasoning. In order to describe a deductive system, a (formal) language system must first be in place, consisting of (well-formed) formulas, strings of symbols constructed according to some prescribed syntax. With the language in place, reasonin ...
Propositional Logic: Part I - Semantics
... This (p |= b) is an invalid argument. Why use it? The real argument is: p, ¬p |= b which is a valid argument. Why is it valid? There is no counter example where p ∧ ¬p is true and b is false. Ex falso quod libet! i.e. “From false all things are possible!” ¬p is an implicit assumption in the verbal a ...
... This (p |= b) is an invalid argument. Why use it? The real argument is: p, ¬p |= b which is a valid argument. Why is it valid? There is no counter example where p ∧ ¬p is true and b is false. Ex falso quod libet! i.e. “From false all things are possible!” ¬p is an implicit assumption in the verbal a ...
Natural Deduction Calculus for Quantified Propositional Linear
... While the propositional quantification does not add any expressiveness to the classical logic QPTL is more expressive than PLTL presenting the same potential of expressiveness as linear-time µ-calculus (linear-time propositional temporal fixpoint logic) [Kaivola (1997)], ETL (propositional linear-ti ...
... While the propositional quantification does not add any expressiveness to the classical logic QPTL is more expressive than PLTL presenting the same potential of expressiveness as linear-time µ-calculus (linear-time propositional temporal fixpoint logic) [Kaivola (1997)], ETL (propositional linear-ti ...
INF3170 Logikk Spring 2011 Homework #8 Problems 2–6
... ◦ c. Do all cases in the induction proof above. d. Use the definition of [[−]]v to compute [[φ ∨ ¬φ]]v . Conclude that RAA does not follow from the other deduction rules. e. Is this semantics complete? That is, is it the case that Γ I φ ⇒ Γ ` φ for Γ a finite set of formulas? Justify your answer. 8 ...
... ◦ c. Do all cases in the induction proof above. d. Use the definition of [[−]]v to compute [[φ ∨ ¬φ]]v . Conclude that RAA does not follow from the other deduction rules. e. Is this semantics complete? That is, is it the case that Γ I φ ⇒ Γ ` φ for Γ a finite set of formulas? Justify your answer. 8 ...
Section 6.1 How Do We Reason? We make arguments, where an
... followed by a single statement, called the conclusion. The hope is that we make valid arguments, where an argument is valid if the truth of the premises implies the truth of the conclusion. We can use rules of logic to make valid arguments. The most common rule of logic is modus ponens (mode that af ...
... followed by a single statement, called the conclusion. The hope is that we make valid arguments, where an argument is valid if the truth of the premises implies the truth of the conclusion. We can use rules of logic to make valid arguments. The most common rule of logic is modus ponens (mode that af ...
4 slides/page
... • epistemic logic: for reasoning about knowledge The simplest logic (on which all the rest are based) is propositional logic. It is intended to capture features of arguments such as the following: Borogroves are mimsy whenever it is brillig. It is now brillig and this thing is a borogrove. Hence thi ...
... • epistemic logic: for reasoning about knowledge The simplest logic (on which all the rest are based) is propositional logic. It is intended to capture features of arguments such as the following: Borogroves are mimsy whenever it is brillig. It is now brillig and this thing is a borogrove. Hence thi ...
Book Question Set #1: Ertel, Chapter 2: Propositional Logic
... d. ( A IMPLIES B ), where A and B are a propositional variable An implication that, ‘if A then B’ (also known as material implication) e. ( A EQUIVALENT-TO B ), where A and B are a propositional value A statement of equivalence where, ‘A if and only if B’ 6.) What does it mean for two propositional ...
... d. ( A IMPLIES B ), where A and B are a propositional variable An implication that, ‘if A then B’ (also known as material implication) e. ( A EQUIVALENT-TO B ), where A and B are a propositional value A statement of equivalence where, ‘A if and only if B’ 6.) What does it mean for two propositional ...
Homework 5
... (1) Reduce these P 2 formulas to purely propositional formulas. (a) (∀p) p ⊃ ⊥ (b) (∀p)(∀q) ((∼p ∨ q)⊃(p⊃q)) (c) (∀p)(∀q) ((p⊃p ∨ q) ∧ (p ∧ q⊃p)) (2) Give Refinement logic rules for P 2 . (3) Construct an example of a formula that is satisfiable in a denumerable universe but not in any finite one (e ...
... (1) Reduce these P 2 formulas to purely propositional formulas. (a) (∀p) p ⊃ ⊥ (b) (∀p)(∀q) ((∼p ∨ q)⊃(p⊃q)) (c) (∀p)(∀q) ((p⊃p ∨ q) ∧ (p ∧ q⊃p)) (2) Give Refinement logic rules for P 2 . (3) Construct an example of a formula that is satisfiable in a denumerable universe but not in any finite one (e ...
Propositional Logic
... (A1) (X (Y X)) (A2) ((X (Y Z)) ((X Y) (X Z))) (A3) ((X Y) ((X Y) X)) ...
... (A1) (X (Y X)) (A2) ((X (Y Z)) ((X Y) (X Z))) (A3) ((X Y) ((X Y) X)) ...
Predicate Calculus pt. 2
... finite subset of T is satisfiable and enlarging T to a maximal set of propositional formulas T ∗ (in the same variables) so that every finite subset of T ∗ is satisfiable and let µ(p) = W ⇐⇒ p ∈ T ∗ . Show that µ makes all formulas in T true. Exercise 2 A (symmetric, irreflexive) graph G = (V, E) co ...
... finite subset of T is satisfiable and enlarging T to a maximal set of propositional formulas T ∗ (in the same variables) so that every finite subset of T ∗ is satisfiable and let µ(p) = W ⇐⇒ p ∈ T ∗ . Show that µ makes all formulas in T true. Exercise 2 A (symmetric, irreflexive) graph G = (V, E) co ...
Bound and Free Variables Theorems and Proofs
... • syntax: what are the valid formulas • semantics: under what circumstances is a formula true • proof theory/ axiomatization: rules for proving a formula true Truth and provability are quite different. • What is provable depends on the axioms and inference rules you use • Provability is a mechanical ...
... • syntax: what are the valid formulas • semantics: under what circumstances is a formula true • proof theory/ axiomatization: rules for proving a formula true Truth and provability are quite different. • What is provable depends on the axioms and inference rules you use • Provability is a mechanical ...
Definition - Rogelio Davila
... (A1) (X (Y X)) (A2) ((X (Y Z)) ((X Y) (X Z))) (A3) ((X Y) ((X Y) X)) ...
... (A1) (X (Y X)) (A2) ((X (Y Z)) ((X Y) (X Z))) (A3) ((X Y) ((X Y) X)) ...
Lecture_ai_3 - WordPress.com
... • Interpretation of implication is T if the previous statement has T value • Interpretation of Biconditionalis T only when symbols on the both sides are either T or F ,otherwise F ...
... • Interpretation of implication is T if the previous statement has T value • Interpretation of Biconditionalis T only when symbols on the both sides are either T or F ,otherwise F ...
Slides - UCSD CSE
... Assume, to the contrary that ______________________ (~p) Then, __________________________________ (formula that follows from p) Now, _________________________ (p " ~p) ...
... Assume, to the contrary that ______________________ (~p) Then, __________________________________ (formula that follows from p) Now, _________________________ (p " ~p) ...