Modus ponens
... of definition" and the "rule of substitution". Modus ponens allows one to eliminate a conditional statement from a logical proof or argument (the antecedents) and thereby not carry these antecedents forward in an everlengthening string of symbols; for this reason modus ponens is sometimes called the ...
... of definition" and the "rule of substitution". Modus ponens allows one to eliminate a conditional statement from a logical proof or argument (the antecedents) and thereby not carry these antecedents forward in an everlengthening string of symbols; for this reason modus ponens is sometimes called the ...
Propositional/First
... under all interpretations, no matter what the world is actually like or what the semantics is. Example: “It’s raining or it’s not raining.” • An inconsistent sentence or contradiction is a sentence that is False under all interpretations. The world is never like what it describes, as in “It’s rainin ...
... under all interpretations, no matter what the world is actually like or what the semantics is. Example: “It’s raining or it’s not raining.” • An inconsistent sentence or contradiction is a sentence that is False under all interpretations. The world is never like what it describes, as in “It’s rainin ...
slides - Computer and Information Science
... • Given a particular formula, can you tell if it is true or not? • No — you usually need to know the truth values of the component atomic propositions in order to be able to tell whether a formula is true. • Definition: A valuation is a function which assigns a truth value to each primitive proposit ...
... • Given a particular formula, can you tell if it is true or not? • No — you usually need to know the truth values of the component atomic propositions in order to be able to tell whether a formula is true. • Definition: A valuation is a function which assigns a truth value to each primitive proposit ...
Notes
... We have seen that type inference is the process of inferring a type for a given λ-term. Under the Curry– Howard isomorphism, this is the same as determining what theorem a given proof proves. Theorem proving, on the other hand, is going in the opposite direction: Given a formula, does it have a proo ...
... We have seen that type inference is the process of inferring a type for a given λ-term. Under the Curry– Howard isomorphism, this is the same as determining what theorem a given proof proves. Theorem proving, on the other hand, is going in the opposite direction: Given a formula, does it have a proo ...
Predicate logic - Teaching-WIKI
... • Interpretation – Maps symbols of the formal language (predicates, functions, variables, constants) onto objects, relations, and functions of the “world” (formally: Domain, relational Structure, or Universe) • Valuation – Assigns domain objects to variables – The Valuation function can be used for ...
... • Interpretation – Maps symbols of the formal language (predicates, functions, variables, constants) onto objects, relations, and functions of the “world” (formally: Domain, relational Structure, or Universe) • Valuation – Assigns domain objects to variables – The Valuation function can be used for ...
Predicate logic
... • Interpretation – Maps symbols of the formal language (predicates, functions, variables, constants) onto objects, relations, and functions of the “world” (formally: Domain, relational Structure, or Universe) • Valuation – Assigns domain objects to variables – The Valuation function can be used for ...
... • Interpretation – Maps symbols of the formal language (predicates, functions, variables, constants) onto objects, relations, and functions of the “world” (formally: Domain, relational Structure, or Universe) • Valuation – Assigns domain objects to variables – The Valuation function can be used for ...
Basic Logic - Progetto e
... a conjunction is expressed as “P and Q” but can be also expressed by “P, but Q”, and “P, however Q”, “P, although Q”, “P, while Q” given that the compound meaning is just given b ...
... a conjunction is expressed as “P and Q” but can be also expressed by “P, but Q”, and “P, however Q”, “P, although Q”, “P, while Q” given that the compound meaning is just given b ...
PDF
... theorem A → A, followed by an axiom instance, then C, then the result of modus ponens, then an axiom instance, and finally two applications of modus ponens. Note the second to the last formula is just (A → A) → (A → B). – If C and C → B are axioms or in ∆, then ∆ `i A → B based on the deduction C, C ...
... theorem A → A, followed by an axiom instance, then C, then the result of modus ponens, then an axiom instance, and finally two applications of modus ponens. Note the second to the last formula is just (A → A) → (A → B). – If C and C → B are axioms or in ∆, then ∆ `i A → B based on the deduction C, C ...
F - Teaching-WIKI
... • One of the simplest and most common logic – The core of (almost) all other logics ...
... • One of the simplest and most common logic – The core of (almost) all other logics ...
T - STI Innsbruck
... • One of the simplest and most common logic – The core of (almost) all other logics ...
... • One of the simplest and most common logic – The core of (almost) all other logics ...
(P Q). - Snistnote
... derivation is called a deduction or formal proof. In a formal proof, every rule of inference that is used at any stage in the derivation is acknowledged. ...
... derivation is called a deduction or formal proof. In a formal proof, every rule of inference that is used at any stage in the derivation is acknowledged. ...
Exam 2 study guide
... Proving a formula of the form φ→ ψ, where the conditional φ→ψ is provable: first prove the conditional φ→ψ, then Necessitate, then distribute the over the → using K . Proving a formula of the form ◊φ→◊ψ, where the conditional φ→ψ is provable. As above, but use K◊. Proving a formula of the form φ ...
... Proving a formula of the form φ→ ψ, where the conditional φ→ψ is provable: first prove the conditional φ→ψ, then Necessitate, then distribute the over the → using K . Proving a formula of the form ◊φ→◊ψ, where the conditional φ→ψ is provable. As above, but use K◊. Proving a formula of the form φ ...
Predicate Logic
... rhs is false This suggests that formulas in PNF are very sensitive to the order of the quantifiers. Q: Is the following formula valid? 8x9y(M (x) ^ F (y)) $ 9y8x(M (x) ^ F (y)) ...
... rhs is false This suggests that formulas in PNF are very sensitive to the order of the quantifiers. Q: Is the following formula valid? 8x9y(M (x) ^ F (y)) $ 9y8x(M (x) ^ F (y)) ...
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 ...