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... Solution: Let p and q be the statements that A is a knight and B is a knight, respectively. So, then p represents the proposition that A is a knave and q that B is a knave. If A is a knight, then p is true. Since knights tell the truth, q must also be true. Then (p ∧ q)∨ ( p ∧ q) would have t ...
... Solution: Let p and q be the statements that A is a knight and B is a knight, respectively. So, then p represents the proposition that A is a knave and q that B is a knave. If A is a knight, then p is true. Since knights tell the truth, q must also be true. Then (p ∧ q)∨ ( p ∧ q) would have t ...
Propositional Logic
... • Hard to identify “individuals” (e.g., Mary, 3) • Can’t directly talk about properties of individuals or relations between individuals (e.g., “Bill is tall”) • Generalizations, patterns, regularities can’t easily be represented (e.g., “all triangles have 3 sides”) • First-Order Logic (abbreviated F ...
... • Hard to identify “individuals” (e.g., Mary, 3) • Can’t directly talk about properties of individuals or relations between individuals (e.g., “Bill is tall”) • Generalizations, patterns, regularities can’t easily be represented (e.g., “all triangles have 3 sides”) • First-Order Logic (abbreviated F ...
Deep Sequent Systems for Modal Logic
... Given a formula A, its negation Ā is defined as usual using the De Morgan laws, A ⊃ B is defined as Ā∨B and ⊥ is defined as p∧ p̄ for some proposition p. A frame is a pair (S, →) of a nonempty set S of states and a binary relation → on it. A model M is a triple (S, →, V ) where (S, →) is a frame a ...
... Given a formula A, its negation Ā is defined as usual using the De Morgan laws, A ⊃ B is defined as Ā∨B and ⊥ is defined as p∧ p̄ for some proposition p. A frame is a pair (S, →) of a nonempty set S of states and a binary relation → on it. A model M is a triple (S, →, V ) where (S, →) is a frame a ...
Lesson 2
... A set of formulas {A1,…,An} is satisfiable iff there is a valuation v such that v is a model of every formula Ai, i = 1,...,n. The valuation v is then a model of the set {A1,…,An}. Mathematical Logic ...
... A set of formulas {A1,…,An} is satisfiable iff there is a valuation v such that v is a model of every formula Ai, i = 1,...,n. The valuation v is then a model of the set {A1,…,An}. Mathematical Logic ...
From proof theory to theories theory
... theorems, and thus require a theory, has be given up and proofs have been studied for for their own sake. A typical example is linear logic [24]. The thesis we shall develop in this paper is that there is another possible way to go for proof theory: modify the notion of theory so that it can be prop ...
... theorems, and thus require a theory, has be given up and proofs have been studied for for their own sake. A typical example is linear logic [24]. The thesis we shall develop in this paper is that there is another possible way to go for proof theory: modify the notion of theory so that it can be prop ...
Lecture Notes 3
... Entered ^ Drove(john,car(john),house(john)) – OK? No – the truth functional connectives connect sentences, not predicates Entered(john,car(john)) ^ Drove(john,house(john)) – This is OK ...
... Entered ^ Drove(john,car(john),house(john)) – OK? No – the truth functional connectives connect sentences, not predicates Entered(john,car(john)) ^ Drove(john,house(john)) – This is OK ...
p q
... Common phrasings for the biconditional • p if and only if q • p is necessary and equivalent for q • p is equivalent to q ...
... Common phrasings for the biconditional • p if and only if q • p is necessary and equivalent for q • p is equivalent to q ...
Implicative Formulae in the Vroofs as Computations” Analogy
... 8. A formula is either an atomic proposition or the product A8B of two formulae. An intuitionistic sequent has the syntactic structure l? I- B where r is a finite (possibly ...
... 8. A formula is either an atomic proposition or the product A8B of two formulae. An intuitionistic sequent has the syntactic structure l? I- B where r is a finite (possibly ...
1 Chapter 9: Deductive Reasoning
... Implication (if p then q): The statement if p then q is an implication. It is true when p and q, called the antecedent and consequent respectively, are true and false when p is true but q is false. It is also considered to be true when the antecedent is false. For example: If you look directly at th ...
... Implication (if p then q): The statement if p then q is an implication. It is true when p and q, called the antecedent and consequent respectively, are true and false when p is true but q is false. It is also considered to be true when the antecedent is false. For example: If you look directly at th ...
P Q
... substituted for every occurrence of a symbol in a proposition that is an axiom or theorem already known to be true For instance, (BB)B may have the expression A substituted for B to produce (AA)A ...
... substituted for every occurrence of a symbol in a proposition that is an axiom or theorem already known to be true For instance, (BB)B may have the expression A substituted for B to produce (AA)A ...
![[Ch 3, 4] Logic and Proofs (2) 1. Valid and Invalid Arguments (§2.3](http://s1.studyres.com/store/data/014954007_1-d36c768aba23f0b4aa633cb9a2a27ee2-300x300.png)
