Predicate_calculus
... calculus or first-order functional calculus, as distinct from calculi containing quantifiers over predicates and corresponding convolution axioms, expressing the existence of the respective predicates. Such a kind of calculus, which already does not have a pure logical character, is often called a h ...
... calculus or first-order functional calculus, as distinct from calculi containing quantifiers over predicates and corresponding convolution axioms, expressing the existence of the respective predicates. Such a kind of calculus, which already does not have a pure logical character, is often called a h ...
Knowledge Representation
... • There is a precise meaning to expressions in predicate logic. • Like in propositional logic, it is all about determining whether something is true or false. • X P(X) means that P(X) must be true for every object X in the domain of interest. • X P(X) means that P(X) must be true for at least on ...
... • There is a precise meaning to expressions in predicate logic. • Like in propositional logic, it is all about determining whether something is true or false. • X P(X) means that P(X) must be true for every object X in the domain of interest. • X P(X) means that P(X) must be true for at least on ...
(formal) logic? - Departamento de Informática
... Much of standard mathematics can be done within the framework of intuitionistic logic, but the task is very difficult, so mathematicians use methods of classical logic (as proofs by contradiction). However the philosophy behind intuitionistic logic is appealing for a computer scientist. For an intuiti ...
... Much of standard mathematics can be done within the framework of intuitionistic logic, but the task is very difficult, so mathematicians use methods of classical logic (as proofs by contradiction). However the philosophy behind intuitionistic logic is appealing for a computer scientist. For an intuiti ...
lecture notes
... Example 2: Consider the following hypothesis: 1. It is not sunny this afternoon and it is colder than yesterday. 2. We will go swimming only if it is sunny. 3. If we do not go swimming, then we will take a canoe trip. 4. If we take a canoe trip, then we will be home by sunset. From this hypothesis, ...
... Example 2: Consider the following hypothesis: 1. It is not sunny this afternoon and it is colder than yesterday. 2. We will go swimming only if it is sunny. 3. If we do not go swimming, then we will take a canoe trip. 4. If we take a canoe trip, then we will be home by sunset. From this hypothesis, ...
ppt
... • A propositional sentence is valid (TRUE) if and only if it is true under all possible interpretations in all possible domains. • For example: If Today_Is_Tuesday Then We_Have_Class ...
... • A propositional sentence is valid (TRUE) if and only if it is true under all possible interpretations in all possible domains. • For example: If Today_Is_Tuesday Then We_Have_Class ...
Chapter 1: The Foundations: Logic and Proofs
... • The area of logic that deals with propositions is called the propositional calculus or propositional logic. ...
... • The area of logic that deals with propositions is called the propositional calculus or propositional logic. ...
MATHEMATICS INDUCTION AND BINOM THEOREM
... form of n P(n), in which the whole discussion is about positive integers sets Three steps to prove (using mathematics induction) that “P(n) is true for all n positive integers”: 1. Basic step: prove that P(1) is true 2. Inductive step: Assumed that P(k) is true, it can be shown that P(k+1) is tru ...
... form of n P(n), in which the whole discussion is about positive integers sets Three steps to prove (using mathematics induction) that “P(n) is true for all n positive integers”: 1. Basic step: prove that P(1) is true 2. Inductive step: Assumed that P(k) is true, it can be shown that P(k+1) is tru ...
sample cheatsheet
... Proofs of equivalence: When conjectures are compound propositions, we may prove or disprove them by proving or disproving their equivalencies. If and only if (↔) : In order to prove this you must prove p→q and q→p (p←q) are both true using the above methods. Uniqueness: Is generally performed by con ...
... Proofs of equivalence: When conjectures are compound propositions, we may prove or disprove them by proving or disproving their equivalencies. If and only if (↔) : In order to prove this you must prove p→q and q→p (p←q) are both true using the above methods. Uniqueness: Is generally performed by con ...
2/TRUTH-FUNCTIONS
... ForclassDiscussionsOnly.Teacher.Armand.L.Tan.AssociateProfessor. PhilosophyDepartment.SillimanUniversity s6. S.variable: letter use to symbolize statements such as p, q, r, and s. Statements are either simple such as `Roses are Red’ or compound: `Aristotle is Greek and Russell is English.’ Statement ...
... ForclassDiscussionsOnly.Teacher.Armand.L.Tan.AssociateProfessor. PhilosophyDepartment.SillimanUniversity s6. S.variable: letter use to symbolize statements such as p, q, r, and s. Statements are either simple such as `Roses are Red’ or compound: `Aristotle is Greek and Russell is English.’ Statement ...
Lesson 12
... 1. A, B are not formulas, but meta-symbols denoting any formula. Each axiom schema denotes an infinite class of formulas of a given form. If axioms were specified by concrete formulas, like 1. p (q p) 2. (p (q r)) ((p q) (p r)) 3. (q p) (p q) we would have to extend the set o ...
... 1. A, B are not formulas, but meta-symbols denoting any formula. Each axiom schema denotes an infinite class of formulas of a given form. If axioms were specified by concrete formulas, like 1. p (q p) 2. (p (q r)) ((p q) (p r)) 3. (q p) (p q) we would have to extend the set o ...
Logic Agents and Propositional Logic
... A sentence is valid if it is true in all models. e.g., True, A A, A A, (A (A B)) B (tautologies) Validity is connected to entailment via the Deduction Theorem: KB ╞ α if and only if (KB α) is valid A sentence is satisfiable if it is true in some model. e.g., A B, C are satisfi ...
... A sentence is valid if it is true in all models. e.g., True, A A, A A, (A (A B)) B (tautologies) Validity is connected to entailment via the Deduction Theorem: KB ╞ α if and only if (KB α) is valid A sentence is satisfiable if it is true in some model. e.g., A B, C are satisfi ...
Propositions as Types - Informatics Homepages Server
... consideration at one moment must be bounded (“We cannot tell at a glance whether 9999999999999999 and 999999999999999 are the same”). Later, Gandy [18] would point out that Turing’s argument amounts to a theorem asserting that any computation a human with paper and pencil can perform can also be per ...
... consideration at one moment must be bounded (“We cannot tell at a glance whether 9999999999999999 and 999999999999999 are the same”). Later, Gandy [18] would point out that Turing’s argument amounts to a theorem asserting that any computation a human with paper and pencil can perform can also be per ...
HW-04 due 02/10
... P: I am awake Q: I work hard R: I dream of home Represent each of the following sentences as logical expressions: a. I dream of home only if I am not working hard b. Working hard is sufficient for me not to dream of home c. Being awake is necessary for me to work hard ...
... P: I am awake Q: I work hard R: I dream of home Represent each of the following sentences as logical expressions: a. I dream of home only if I am not working hard b. Working hard is sufficient for me not to dream of home c. Being awake is necessary for me to work hard ...
T - UTH e
... Example: What are the types of A and B? 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 ...
... Example: What are the types of A and B? 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 ...
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). ...
full text (.pdf)
... Proof. We show (ii) ) (i) ) (iii) ) (ii). The rst implication is immediate from the soundness of PHL over relational models. For the second implication, let 2 f0 1g be any input string. Build a relational model of PHL as follows: the elements are the pre xes of the formula is true at if = and th ...
... Proof. We show (ii) ) (i) ) (iii) ) (ii). The rst implication is immediate from the soundness of PHL over relational models. For the second implication, let 2 f0 1g be any input string. Build a relational model of PHL as follows: the elements are the pre xes of the formula is true at if = and th ...
(A B) |– A
... 1. A, B are not formulas, but meta-symbols denoting any formula. Each axiom schema denotes an infinite class of formulas of a given form. If axioms were specified by concrete formulas, like 1. p (q p) 2. (p (q r)) ((p q) (p r)) 3. (q p) (p q) we would have to extend the set o ...
... 1. A, B are not formulas, but meta-symbols denoting any formula. Each axiom schema denotes an infinite class of formulas of a given form. If axioms were specified by concrete formulas, like 1. p (q p) 2. (p (q r)) ((p q) (p r)) 3. (q p) (p q) we would have to extend the set o ...
Logic
... statements are claimed to follow from others, this may in fact not be the case. • Example: “If I win the lottery, then I’m happy. However, I did not win the lottery. Therefore, I am not happy.” • A piece of reasoning is valid if the statements that are claimed to follow from previous ones do indeed ...
... statements are claimed to follow from others, this may in fact not be the case. • Example: “If I win the lottery, then I’m happy. However, I did not win the lottery. Therefore, I am not happy.” • A piece of reasoning is valid if the statements that are claimed to follow from previous ones do indeed ...