Logic is a discipline that studies the principles and methods used in
... Predicate Logic: Existential Quantifier Suppose P(x) is a predicate on some universe of discourse. The existential quantification of P(x) is the proposition: “There exists at least one x in the universe of discourse such that P(x) is true.” ∃ x P(x) reads “for some x, P(x)” or “There exists x, P(x) ...
... Predicate Logic: Existential Quantifier Suppose P(x) is a predicate on some universe of discourse. The existential quantification of P(x) is the proposition: “There exists at least one x in the universe of discourse such that P(x) is true.” ∃ x P(x) reads “for some x, P(x)” or “There exists x, P(x) ...
Predicate logic - Teaching-WIKI
... • We'd like to conclude that Jan will get wet. But each of these sentences would just be a represented by some proposition, say P, Q and R. What relationship is there between these propositions? We can say P /\ Q → R Then, given P /\ Q, we could indeed conclude R. But now, suppose we were told Pat i ...
... • We'd like to conclude that Jan will get wet. But each of these sentences would just be a represented by some proposition, say P, Q and R. What relationship is there between these propositions? We can say P /\ Q → R Then, given P /\ Q, we could indeed conclude R. But now, suppose we were told Pat i ...
Predicate logic
... • We'd like to conclude that Jan will get wet. But each of these sentences would just be a represented by some proposition, say P, Q and R. What relationship is there between these propositions? We can say P /\ Q → R Then, given P /\ Q, we could indeed conclude R. But now, suppose we were told Pat i ...
... • We'd like to conclude that Jan will get wet. But each of these sentences would just be a represented by some proposition, say P, Q and R. What relationship is there between these propositions? We can say P /\ Q → R Then, given P /\ Q, we could indeed conclude R. But now, suppose we were told Pat i ...
Philosophy 240: Symbolic Logic
... < We want to analyze the component parts of the Spanish expressions, and how they interact to form true or false sentences. < The T-schema, by itself, does not provide that kind of explanation. ...
... < We want to analyze the component parts of the Spanish expressions, and how they interact to form true or false sentences. < The T-schema, by itself, does not provide that kind of explanation. ...
A Simple Exposition of Gödel`s Theorem
... In October 1997 I was asked to join in a discussion of the Gödelian argument at an undergraduate philosophy club in King's College, London; and I was asked to preface it with a very simple exposition of Gödel's (first) Theorem at a level at which first-year students could understand. Although there ...
... In October 1997 I was asked to join in a discussion of the Gödelian argument at an undergraduate philosophy club in King's College, London; and I was asked to preface it with a very simple exposition of Gödel's (first) Theorem at a level at which first-year students could understand. Although there ...
Overview of proposition and predicate logic Introduction
... have no meaning by themselves, semantics can only be given to expressions by a function which maps syntactical objects to objects in some real world. A world consists of – a universe U of objects, – a collection P of predicates on U, i.e., subsets of (ordered n-tuples of) objects of U, – a collectio ...
... have no meaning by themselves, semantics can only be given to expressions by a function which maps syntactical objects to objects in some real world. A world consists of – a universe U of objects, – a collection P of predicates on U, i.e., subsets of (ordered n-tuples of) objects of U, – a collectio ...
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 some way to represent 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 some way to represent the fact that all ...
methods of proof
... Theorem is a statement that can be shown to be true. In mathematical writing, the term theorem is usually reserved for a statement that is considered at least somewhat important. A theorem may be the universal quantification of a conditional statement with one or more premises and a conclusion. We d ...
... Theorem is a statement that can be shown to be true. In mathematical writing, the term theorem is usually reserved for a statement that is considered at least somewhat important. A theorem may be the universal quantification of a conditional statement with one or more premises and a conclusion. We d ...
āgārjuna’s Logic N 8 8.1 N
... of b and b is b, we have it that ν(B ¬B) = b. Further, it follows from our supposition that ν(¬A) = f. Since the least upper bound of b and f is b, we have it that ν(¬A (B ¬B)) = b. But that’s equivalent to (A ⊃ (B ¬B), and so our premise is designated. But ν(¬A) = f, which is undesignated. So we ha ...
... of b and b is b, we have it that ν(B ¬B) = b. Further, it follows from our supposition that ν(¬A) = f. Since the least upper bound of b and f is b, we have it that ν(¬A (B ¬B)) = b. But that’s equivalent to (A ⊃ (B ¬B), and so our premise is designated. But ν(¬A) = f, which is undesignated. So we ha ...
Semantics of PL
... 1. Universe. To interpret and we need to know what these quantifiers range over. In formal semantics, interpret the universe as a non-empty set of objects. So it has to contain at least one thing, but there is no upper limit on the number or type of things it contains. Our book has ‘finite inter ...
... 1. Universe. To interpret and we need to know what these quantifiers range over. In formal semantics, interpret the universe as a non-empty set of objects. So it has to contain at least one thing, but there is no upper limit on the number or type of things it contains. Our book has ‘finite inter ...
Lecture 3
... • “If you clean the car then you can go out” • Could we infer either of the following? – “if you don't clean the car then you can't go out” or – “if you were allowed out, then you must have cleaned the car”. ...
... • “If you clean the car then you can go out” • Could we infer either of the following? – “if you don't clean the car then you can't go out” or – “if you were allowed out, then you must have cleaned the car”. ...
Jacques Herbrand (1908 - 1931) Principal writings in logic
... ES(A,p) that makes the expansion true and assigns the numerical value q to the constant c. œxœy∑zı(x,y,z) expresses the existence, for any p and q, of interpretations that make ES(A,p) true, and give the constant c the value q. If the theory is a true theory of arithmetic, then œxœy∑zı(x,y,z) is tru ...
... ES(A,p) that makes the expansion true and assigns the numerical value q to the constant c. œxœy∑zı(x,y,z) expresses the existence, for any p and q, of interpretations that make ES(A,p) true, and give the constant c the value q. If the theory is a true theory of arithmetic, then œxœy∑zı(x,y,z) is tru ...
ppt
... – If S is an element of S, then S is a member of itself and should not be in S. – If S is not an element of S, then S is not a member of itself, and should be in S. ...
... – If S is an element of S, then S is a member of itself and should not be in S. – If S is not an element of S, then S is not a member of itself, and should be in S. ...
Logical Consequence by Patricia Blanchette Basic Question (BQ
... Because of the expressive power of higher order logics, they can say things about a formal system S which are either true or false of that system, but which can not be derived using the deductive apparatus of that system. This is the basic insight captured in Gödel’s Incompleteness Theorem, but it i ...
... Because of the expressive power of higher order logics, they can say things about a formal system S which are either true or false of that system, but which can not be derived using the deductive apparatus of that system. This is the basic insight captured in Gödel’s Incompleteness Theorem, but it i ...
10a
... • Logical inference creates new sentences that logically follow from a set of sentences (KB) • An inference rule is sound if every sentence X it produces when operating on a KB logically follows from the KB –i.e., inference rule creates no contradictions • An inference rule is complete if it can pro ...
... • Logical inference creates new sentences that logically follow from a set of sentences (KB) • An inference rule is sound if every sentence X it produces when operating on a KB logically follows from the KB –i.e., inference rule creates no contradictions • An inference rule is complete if it can pro ...
Chapter 5 - Stanford Lagunita
... These two criteria pull in opposite directions. Typically, the more significant the step, the harder it is to follow. Good style requires a reasonable balance between the two. And that in turn requires some sense of who your audience is. For example, if you and your audience have been working with l ...
... These two criteria pull in opposite directions. Typically, the more significant the step, the harder it is to follow. Good style requires a reasonable balance between the two. And that in turn requires some sense of who your audience is. For example, if you and your audience have been working with l ...
T - RTU
... in First-Order Logic The semantics of first-order logic provide a basis for a formal theory of logical inference. The ability to infer new correct expressions from a set of true assertions is very important feature of first-order logic. These new expressions are correct in that they are consistent w ...
... in First-Order Logic The semantics of first-order logic provide a basis for a formal theory of logical inference. The ability to infer new correct expressions from a set of true assertions is very important feature of first-order logic. These new expressions are correct in that they are consistent w ...
Lecture 2
... Modelling English propositions • A proposition can be interpreted as being either true or false. For example: • “Henry VIII had one son and Cleopatra had two” • We wish to translate English propositions to Boolean expressions because: – English is ambiguous, computers require logical clarity. – We ...
... Modelling English propositions • A proposition can be interpreted as being either true or false. For example: • “Henry VIII had one son and Cleopatra had two” • We wish to translate English propositions to Boolean expressions because: – English is ambiguous, computers require logical clarity. – We ...
q - Mona Shores Blogs
... Example • If you get a D- or above in Geometry, then you will get credit for the class. • Your final grade is a D. • Therefore… – You will get credit for this class! ...
... Example • If you get a D- or above in Geometry, then you will get credit for the class. • Your final grade is a D. • Therefore… – You will get credit for this class! ...
A Brief Introduction to Propositional Logic
... • If the truth value of a sentence is 1, the truth value of its negation is 0. If the truth value of a sentence is 0, the truth value of its negation is 1. • The truth value of a conjunction is true if and only if the truth value of its conjuncts are both true; otherwise, the truth value is false. • ...
... • If the truth value of a sentence is 1, the truth value of its negation is 0. If the truth value of a sentence is 0, the truth value of its negation is 1. • The truth value of a conjunction is true if and only if the truth value of its conjuncts are both true; otherwise, the truth value is false. • ...
Homework #6
... If Alice is happy Jack either sings in the shower or plays golf regularly. If Alice is happy, she tends the plants and Jack is happy. If Jack is happy, he sings in the shower. If Alice is happy and tends the plants then Jack sings in the shower. None of the above ...
... If Alice is happy Jack either sings in the shower or plays golf regularly. If Alice is happy, she tends the plants and Jack is happy. If Jack is happy, he sings in the shower. If Alice is happy and tends the plants then Jack sings in the shower. None of the above ...
Chapter 7
... • We can use symbols P, Q, and R to denote the three propositions, but this leads us to nowhere because knowledge important to infer R from P and Q (i.e., relationship between being a human and mortality, and the membership relation between Confucius and human class) is not expressed in a way that c ...
... • We can use symbols P, Q, and R to denote the three propositions, but this leads us to nowhere because knowledge important to infer R from P and Q (i.e., relationship between being a human and mortality, and the membership relation between Confucius and human class) is not expressed in a way that c ...
Preferences and Unrestricted Rebut
... papers is the work of Caminada and Amgoud [2], in which a number of rationality postulates are specified: direct consistency, indirect consistency, (conclusion) closure and subargument closure. The authors provide two different approaches for satisfying these postulates: one that applies unrestricte ...
... papers is the work of Caminada and Amgoud [2], in which a number of rationality postulates are specified: direct consistency, indirect consistency, (conclusion) closure and subargument closure. The authors provide two different approaches for satisfying these postulates: one that applies unrestricte ...
Supplement: Conditional statements and basic methods of proof
... my promise regardless of whether I decide to give you a dollar or not. Either way, I’m true to my promise.) So, in order to establish that a conditional statement is true, there’s only one situation that matters: The truth of the hypothesis must ensure the truth of the conclusion. This observation p ...
... my promise regardless of whether I decide to give you a dollar or not. Either way, I’m true to my promise.) So, in order to establish that a conditional statement is true, there’s only one situation that matters: The truth of the hypothesis must ensure the truth of the conclusion. This observation p ...
Slides
... 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 ...