Game Theory: Logic, Set and Summation Notation
... Since we assumed nothing about y except that it was one element of [Y ∩ Z], we can use universal generalization to conclude that (∀x ∈ [Y ∩ Z])[x ∈ Y ∪ Z]. This gives us (1). The proof for (2) is similar. Sets are very useful for expressing order or duplication. For example, to represent a point on ...
... Since we assumed nothing about y except that it was one element of [Y ∩ Z], we can use universal generalization to conclude that (∀x ∈ [Y ∩ Z])[x ∈ Y ∪ Z]. This gives us (1). The proof for (2) is similar. Sets are very useful for expressing order or duplication. For example, to represent a point on ...
Logic of Natural Language Semantics: Presuppositions and
... a proposition, which can be true or false. However, as linguists and philosophers have already noticed, sometimes, a declarative sentence also expresses some extra content on which the truth value of its proposition depends. Such contents are known as presuppositions and they are so called because i ...
... a proposition, which can be true or false. However, as linguists and philosophers have already noticed, sometimes, a declarative sentence also expresses some extra content on which the truth value of its proposition depends. Such contents are known as presuppositions and they are so called because i ...
Conditional Statements
... Example 1: Vertical angles are congruent. can be written as... Conditional Statement: If two angles are vertical, then they are congruent. ...
... Example 1: Vertical angles are congruent. can be written as... Conditional Statement: If two angles are vertical, then they are congruent. ...
Contradiction: means to follow a path toward which a statement
... (Dis)Proof by Counterexample: Finding a value that contradicts the conjecture (by showing that P is true and Q is false for that value). Constructive proof: Finding a value for an existence proof. Non-constructive proof: Showing that a number has the property of the thing trying to be proved and the ...
... (Dis)Proof by Counterexample: Finding a value that contradicts the conjecture (by showing that P is true and Q is false for that value). Constructive proof: Finding a value for an existence proof. Non-constructive proof: Showing that a number has the property of the thing trying to be proved and the ...
sample cheatsheet
... (Dis)Proof by Counterexample: Finding a value that contradicts the conjecture (by showing that P is true and Q is false for that value). Constructive proof: Finding a value for an existence proof. Non-constructive proof: Showing that a number has the property of the thing trying to be proved and the ...
... (Dis)Proof by Counterexample: Finding a value that contradicts the conjecture (by showing that P is true and Q is false for that value). Constructive proof: Finding a value for an existence proof. Non-constructive proof: Showing that a number has the property of the thing trying to be proved and the ...
Logic, deontic. The study of principles of reasoning pertaining to
... philosophers, and again by Leibniz and by Jeremy Bentham, but focused and sustained thought in the field is a twentieth century phenomenon, kindled largely by the writings of G. H. von Wright. Early work was motivated by analogies between the deontic concepts of obligation, permission and prohibitio ...
... philosophers, and again by Leibniz and by Jeremy Bentham, but focused and sustained thought in the field is a twentieth century phenomenon, kindled largely by the writings of G. H. von Wright. Early work was motivated by analogies between the deontic concepts of obligation, permission and prohibitio ...
(draft)
... and a value of type τ . We say that τ is inhabited if you can construct a value of that type (it is possible to construct types for which no values exist; these types are uninhabited) Since the proof is encoded in the structure of the term itself, it turns out that this is very useful for proof carr ...
... and a value of type τ . We say that τ is inhabited if you can construct a value of that type (it is possible to construct types for which no values exist; these types are uninhabited) Since the proof is encoded in the structure of the term itself, it turns out that this is very useful for proof carr ...
Propositional/First
... • Logic is a great knowledge representation language for many AI problems • Propositional logic is the simple foundation and fine for some AI problems • First order logic (FOL) is much more expressive as a KR language and more commonly used in AI • There are many variations: horn logic, higher order ...
... • Logic is a great knowledge representation language for many AI problems • Propositional logic is the simple foundation and fine for some AI problems • First order logic (FOL) is much more expressive as a KR language and more commonly used in AI • There are many variations: horn logic, higher order ...
PREPOSITIONAL LOGIS
... • Logic is a great knowledge representation language for many AI problems • Propositional logic is the simple foundation and fine for some AI problems • First order logic (FOL) is much more expressive as a KR language and more commonly used in AI • There are many variations: horn logic, higher order ...
... • Logic is a great knowledge representation language for many AI problems • Propositional logic is the simple foundation and fine for some AI problems • First order logic (FOL) is much more expressive as a KR language and more commonly used in AI • There are many variations: horn logic, higher order ...
Propositional Logic
... an explicit symbol, R, to represent an individual, Confucius, who is a member of the classes “person” and “mortal.” • To represent other individuals we must introduce separate symbols for each one, with means for representing the fact that all ...
... an explicit symbol, R, to represent an individual, Confucius, who is a member of the classes “person” and “mortal.” • To represent other individuals we must introduce separate symbols for each one, with means for representing the fact that all ...
Document
... one is a notorious liar one is a pokerface, sometimes liar sometimes honest They make the following statements: A says: "I love mathematics." B says: "C always tells the truth." C says: "A hates math." Who is most likely the honest one? ...
... one is a notorious liar one is a pokerface, sometimes liar sometimes honest They make the following statements: A says: "I love mathematics." B says: "C always tells the truth." C says: "A hates math." Who is most likely the honest one? ...
pdf file
... This [kind of semiformal proof] is difficult to define precisely, but what I have in mind is the type of proof that most mathematicians would consider complete and rigorous, but that is not strictly formal in the sense of a purely syntactic derivation using a very precise and circumscribed formal set o ...
... This [kind of semiformal proof] is difficult to define precisely, but what I have in mind is the type of proof that most mathematicians would consider complete and rigorous, but that is not strictly formal in the sense of a purely syntactic derivation using a very precise and circumscribed formal set o ...
A Computationally-Discovered Simplification of the Ontological
... Note that, strictly speaking, we need not have used free logic to reconstruct the argument because we establish at line (3) that our description ıxφ1 is well-defined. Its logic is therefore classical, and the ontological argument proceeds along classical lines.3 Clearly then, the ontological argumen ...
... Note that, strictly speaking, we need not have used free logic to reconstruct the argument because we establish at line (3) that our description ıxφ1 is well-defined. Its logic is therefore classical, and the ontological argument proceeds along classical lines.3 Clearly then, the ontological argumen ...
A Computationally-Discovered Simplification of the Ontological
... Note that, strictly speaking, we need not have used free logic to reconstruct the argument because we establish at line (3) that our description ıxφ1 is well-defined. Its logic is therefore classical, and the ontological argument proceeds along classical lines.3 Clearly then, the ontological argumen ...
... Note that, strictly speaking, we need not have used free logic to reconstruct the argument because we establish at line (3) that our description ıxφ1 is well-defined. Its logic is therefore classical, and the ontological argument proceeds along classical lines.3 Clearly then, the ontological argumen ...
Find the truth value of X ∧ ((Y ⇒ W) ⇔ Z) if X is true, Y is false, and
... C: I enjoy logic interpret the above proposition as an argument in natural English. Logic is a part of mathematics and mathematics is not hard therefore logic is not part of mathematics. In addition, mathematics is hard implying I enjoy logic. Therefore, mathematics is hard and I enjoy logic. ...
... C: I enjoy logic interpret the above proposition as an argument in natural English. Logic is a part of mathematics and mathematics is not hard therefore logic is not part of mathematics. In addition, mathematics is hard implying I enjoy logic. Therefore, mathematics is hard and I enjoy logic. ...
PHILOSOPHY 326 / MATHEMATICS 307 SYMBOLIC LOGIC This
... decision procedures for determining truth functional validity and logical equivalence, and (most importantly) proficiency in constructing proofs in a system of natural deduction for the logic of propositions. This course does not have a fixed and predetermined syllabus. There is core content which w ...
... decision procedures for determining truth functional validity and logical equivalence, and (most importantly) proficiency in constructing proofs in a system of natural deduction for the logic of propositions. This course does not have a fixed and predetermined syllabus. There is core content which w ...
Notes Predicate Logic
... domain, then the statement that follows is true. Propositional logic doesn’t work as well with existential quantification. Example: To say some real number is irrational, we write ∃ x ∈ R, x ∈ / Q. Comment: In propositional logic, we could write ¬( x ∈ R ⇒ x ∈ Q), or in ...
... domain, then the statement that follows is true. Propositional logic doesn’t work as well with existential quantification. Example: To say some real number is irrational, we write ∃ x ∈ R, x ∈ / Q. Comment: In propositional logic, we could write ¬( x ∈ R ⇒ x ∈ Q), or in ...
CS173: Discrete Math
... • P q: “You can take the flight if and only if you buy a ticket” – This statement is true • If you buy a ticket and take the flight • If you do not buy a ticket and you cannot take the flight ...
... • P q: “You can take the flight if and only if you buy a ticket” – This statement is true • If you buy a ticket and take the flight • If you do not buy a ticket and you cannot take the flight ...
chapter1p3 - WordPress.com
... Example: Show that every compound proposition can be put in disjunctive normal form. Solution: Construct the truth table for the proposition. Then an equivalent proposition is the disjunction with n disjuncts (where n is the number of rows for which the formula evaluates to T). Each disjunct has m c ...
... Example: Show that every compound proposition can be put in disjunctive normal form. Solution: Construct the truth table for the proposition. Then an equivalent proposition is the disjunction with n disjuncts (where n is the number of rows for which the formula evaluates to T). Each disjunct has m c ...
Unit-1-B - WordPress.com
... Mathematical Reasoning We need mathematical reasoning to determine whether a mathematical argument is correct or incorrect Mathematical reasoning is important for artificial intelligence systems to reach a conclusion from knowledge and facts. We can use a proof to demonstrate that a particular stat ...
... Mathematical Reasoning We need mathematical reasoning to determine whether a mathematical argument is correct or incorrect Mathematical reasoning is important for artificial intelligence systems to reach a conclusion from knowledge and facts. We can use a proof to demonstrate that a particular stat ...
Phil 2302 Intro to Logic
... premises and conclusions (not just categorical propositions, statements or sentences). Compound syllogisms are more familiar and are more often used than categorical syllogisms, and the rules of their uses are much easier to grasp. There are several kinds of compound syllogisms including hypothetica ...
... premises and conclusions (not just categorical propositions, statements or sentences). Compound syllogisms are more familiar and are more often used than categorical syllogisms, and the rules of their uses are much easier to grasp. There are several kinds of compound syllogisms including hypothetica ...
i Preface
... mystical intellectual power, a power which cannot even be mimicked by a computer. But when one looks at the reasoning which leads to the conclusion that the Gödel sentence is true, one finds nothing remarkable or difficult or unformalizable. What one finds instead is a simple reductio ad absurdum. O ...
... mystical intellectual power, a power which cannot even be mimicked by a computer. But when one looks at the reasoning which leads to the conclusion that the Gödel sentence is true, one finds nothing remarkable or difficult or unformalizable. What one finds instead is a simple reductio ad absurdum. O ...
Conditional Statements and Logic
... • Use the phrase if and only if (sometimes abbreviated: iff) Statement: If an angle is right then it has a measure of 90. Converse: If an angle measures 90, then it is a right angle. Biconditional: An angle is right if and only if it measures 90. ...
... • Use the phrase if and only if (sometimes abbreviated: iff) Statement: If an angle is right then it has a measure of 90. Converse: If an angle measures 90, then it is a right angle. Biconditional: An angle is right if and only if it measures 90. ...
tbmk5ictk6
... propositions. Our argument then has the form: All S are M. All M are P. Therefore, all S are P. Any argument that follows this pattern, or form, is valid. Try it for yourself. Think of any three plural nouns; they do not have to be related to each other. For example, you could use submarines, candy ...
... propositions. Our argument then has the form: All S are M. All M are P. Therefore, all S are P. Any argument that follows this pattern, or form, is valid. Try it for yourself. Think of any three plural nouns; they do not have to be related to each other. For example, you could use submarines, candy ...
Logic and Existential Commitment
... premises are true. To understand logical consequence we must understand how it is possible for sentences to have truth-values other than the ones they actually have. If the conclusion of an invalid argument is Bill Clinton is a human we must think that this sentence could (logically) be false. How c ...
... premises are true. To understand logical consequence we must understand how it is possible for sentences to have truth-values other than the ones they actually have. If the conclusion of an invalid argument is Bill Clinton is a human we must think that this sentence could (logically) be false. How c ...