Section.8.3
... The order of a predicate is 1 if its arguments are terms. Otherwise the order is n + 1 where n is the maximum order of the arguments that are not terms. The order of a function is always 1 since it’s arguments are always terms. Examples. In the wff p(x) q(x, p) the order of p is one and the order ...
... The order of a predicate is 1 if its arguments are terms. Otherwise the order is n + 1 where n is the maximum order of the arguments that are not terms. The order of a function is always 1 since it’s arguments are always terms. Examples. In the wff p(x) q(x, p) the order of p is one and the order ...
PDF - University of Kent
... A valid syllogism is a type of argument that is valid because of its form alone – i.e., because of the particular relationships between the terms and the propositions in it, regardless of the content of the propositions or the truth of the premises. Thus the form of a syllogism is that the conjuncti ...
... A valid syllogism is a type of argument that is valid because of its form alone – i.e., because of the particular relationships between the terms and the propositions in it, regardless of the content of the propositions or the truth of the premises. Thus the form of a syllogism is that the conjuncti ...
Notes on Propositional and Predicate Logic
... One important way of making proofs is using proof by contradiction. Suppose you have a set of premises Γ and a desired conclusion p. Let Γ0 be obtained by adding (not p) to Γ. If it is possible to prove two propositions q and (not q) from Γ0 , then one has a proof of p from Γ. The argument is that i ...
... One important way of making proofs is using proof by contradiction. Suppose you have a set of premises Γ and a desired conclusion p. Let Γ0 be obtained by adding (not p) to Γ. If it is possible to prove two propositions q and (not q) from Γ0 , then one has a proof of p from Γ. The argument is that i ...
Logic and proof
... p ∧ q is false, and p ∨ q is true. What about p → q? It’s true! You could think of it as being “if p is true, then q must be true; if p is false, it doesn’t matter”, or “p being true is a sufficient condition for q to be true”. To maybe get an idea of why we do it this way, suppose we want to prove ...
... p ∧ q is false, and p ∨ q is true. What about p → q? It’s true! You could think of it as being “if p is true, then q must be true; if p is false, it doesn’t matter”, or “p being true is a sufficient condition for q to be true”. To maybe get an idea of why we do it this way, suppose we want to prove ...
Math 3000 Section 003 Intro to Abstract Math Homework 2
... Solution: (a) Possible definition: Two lines in the plane are said to be perpendicular if they form congruent adjacent angles (a T-shape). Possible characterizations: (i) Two lines in the plane are perpendicular if and only if they intersect at an angle of 90 degrees (you can say a “right angle” if ...
... Solution: (a) Possible definition: Two lines in the plane are said to be perpendicular if they form congruent adjacent angles (a T-shape). Possible characterizations: (i) Two lines in the plane are perpendicular if and only if they intersect at an angle of 90 degrees (you can say a “right angle” if ...
PROOFS BY INDUCTION AND CONTRADICTION, AND WELL
... Proofs which use this property are called ‘proofs by induction,’ and usually have a common form. The goal is to prove that some property or statement P(k), holds for all k ∈ N, where the property itself depends on k. First one proves the base case, that P(0) holds (or sometimes P(1) instead of or in ...
... Proofs which use this property are called ‘proofs by induction,’ and usually have a common form. The goal is to prove that some property or statement P(k), holds for all k ∈ N, where the property itself depends on k. First one proves the base case, that P(0) holds (or sometimes P(1) instead of or in ...
Section 1
... Contrapositives, converses, and inverses Definition Consider the implication p q 1. The converse of the implication is 2. The inverse of the implication is 3. The contrapositive of the implication is Proposition 3 1. An implication and its contrapositive are logically equivalent 2. The converse a ...
... Contrapositives, converses, and inverses Definition Consider the implication p q 1. The converse of the implication is 2. The inverse of the implication is 3. The contrapositive of the implication is Proposition 3 1. An implication and its contrapositive are logically equivalent 2. The converse a ...
Predicate Logic
... • The domain of discourse U is all human beings. • “All human beings are mortal.” translates to x (H(x) M(x)) “Sachin is a human being.” translates to H(Sachin) • Therefore, for H(Sachin) M(Sachin) to be true it must be the case that M(Sachin). Later we will show this formally. Thursday, Januar ...
... • The domain of discourse U is all human beings. • “All human beings are mortal.” translates to x (H(x) M(x)) “Sachin is a human being.” translates to H(Sachin) • Therefore, for H(Sachin) M(Sachin) to be true it must be the case that M(Sachin). Later we will show this formally. Thursday, Januar ...
Defending a Dialetheist Response to the Liar`s Paradox
... false, and Joe is intending to do the same regarding Wilma’s words. This seems perfectly intuitive and understandable. Yet on Tarski’s view of truth as a hierarchal predicate, we cannot make sense of such a situation. One of the two statements would have to be of a higher level, declaring the other ...
... false, and Joe is intending to do the same regarding Wilma’s words. This seems perfectly intuitive and understandable. Yet on Tarski’s view of truth as a hierarchal predicate, we cannot make sense of such a situation. One of the two statements would have to be of a higher level, declaring the other ...
Supervaluationism and Classical Logic
... in which we might obtain systems of deduction adequate for supervaluationist consequence based on systems of deduction adequate for classical consequence. Deductions on the systems obtained this way adopt a completely classical form with the exception of a single step. The paper reviews (at least pa ...
... in which we might obtain systems of deduction adequate for supervaluationist consequence based on systems of deduction adequate for classical consequence. Deductions on the systems obtained this way adopt a completely classical form with the exception of a single step. The paper reviews (at least pa ...
Propositional Logic
... Let's add some more logical operators into our language so that we will be able to say more. Use the symbol M for Math is cool, S for Science is cool and R for Reading is cool. The AND operator is M and S. It is true when both M and S are true. The OR operator is M or S. In logic, M or S is true if ...
... Let's add some more logical operators into our language so that we will be able to say more. Use the symbol M for Math is cool, S for Science is cool and R for Reading is cool. The AND operator is M and S. It is true when both M and S are true. The OR operator is M or S. In logic, M or S is true if ...
Logic: Introduction - Department of information engineering and
... • Semantics: To make sure that different implementation of a programming language yield the same results, programming languages need to have a formal semantics. Logic provide the tool to develop such a semantics. Contents ...
... • Semantics: To make sure that different implementation of a programming language yield the same results, programming languages need to have a formal semantics. Logic provide the tool to develop such a semantics. Contents ...
Logic - United States Naval Academy
... Two (compound) expressions are logically equivalent if and only if they have identical truth values for all possible combinations of truth values for the sub-expressions. If A and B are logically equivalent, we write A B . (Another notation for logical equivalence is ; that is, if A and B are lo ...
... Two (compound) expressions are logically equivalent if and only if they have identical truth values for all possible combinations of truth values for the sub-expressions. If A and B are logically equivalent, we write A B . (Another notation for logical equivalence is ; that is, if A and B are lo ...
Mathematical Logic
... Reasoning is a process of deriving new statements (conclusions) from other statements (premises) by argument. For reasoning to be correct, this process should generally preserve truth. That is, the arguments should be valid. How can we be sure our arguments are valid? Reasoning takes place in many d ...
... Reasoning is a process of deriving new statements (conclusions) from other statements (premises) by argument. For reasoning to be correct, this process should generally preserve truth. That is, the arguments should be valid. How can we be sure our arguments are valid? Reasoning takes place in many d ...
Essentials Of Symbolic Logic
... Logic is the science of reasoning. The logician is not concerned with the actual process of inference. The logician is concerned with the correctness of the completed process of inference. Inference is a thought process in which one proposition is arrived at on the basis of other proposition or prop ...
... Logic is the science of reasoning. The logician is not concerned with the actual process of inference. The logician is concerned with the correctness of the completed process of inference. Inference is a thought process in which one proposition is arrived at on the basis of other proposition or prop ...
PROOFS BY INDUCTION AND CONTRADICTION, AND WELL
... Proofs which utilize this property are called ‘proofs by induction,’ and usually have a common form. The goal is to prove that some property or statement P(k), holds for all k ∈ N, where the property itself depends on k. First one proves the base case, that P(1) holds (or sometimes P(0) if one takes ...
... Proofs which utilize this property are called ‘proofs by induction,’ and usually have a common form. The goal is to prove that some property or statement P(k), holds for all k ∈ N, where the property itself depends on k. First one proves the base case, that P(1) holds (or sometimes P(0) if one takes ...
Lectures on Laws of Supply and Demand, Simple and Compound
... Definition A compound proposition is two or more propositions combined by a logical connective. Example 2 “ If Brian and Angela are not both happy then either Brian is not happy or Angela is not happy”. This is an example of a compound proposition. Logic is not concerned with determining the truth ...
... Definition A compound proposition is two or more propositions combined by a logical connective. Example 2 “ If Brian and Angela are not both happy then either Brian is not happy or Angela is not happy”. This is an example of a compound proposition. Logic is not concerned with determining the truth ...
Judgment and consequence relations
... Kleene three valued logic. It is a three valued logic with values 0, 1 and u. Hence a judgment is a boolean combination of “has value 0”, “has value 1” and “has value u”. The truth table of is 1 0, 0 1 and u u. Now, ϕ has value 0 if ϕ has value 1 and ϕ has value 1 if ϕ has value 0. However, if ...
... Kleene three valued logic. It is a three valued logic with values 0, 1 and u. Hence a judgment is a boolean combination of “has value 0”, “has value 1” and “has value u”. The truth table of is 1 0, 0 1 and u u. Now, ϕ has value 0 if ϕ has value 1 and ϕ has value 1 if ϕ has value 0. However, if ...
MATH 311W Wksht 1 • A logical statement is a phrase that is
... NOTE: In logic, we care a lot about when two statements are equivalent, the statements themselves do not always have to be true. When we prove theorems, we will care about statements being true. HW # 1: [Read N&B: pg 2 (definition of statement), and pg 25-27 look at Ex. 1-10, pg 30] 1. Explain wheth ...
... NOTE: In logic, we care a lot about when two statements are equivalent, the statements themselves do not always have to be true. When we prove theorems, we will care about statements being true. HW # 1: [Read N&B: pg 2 (definition of statement), and pg 25-27 look at Ex. 1-10, pg 30] 1. Explain wheth ...
Yablo`s paradox
... ¬Tsn is provable for all n is that we have a uniform proof, i.e., a proof for variable n. Moreover, no finite reasoner ever really applies the ω-rule. The only way that they can know that there is a proof of each α(i) is because they have a uniform method of constructing such proofs. And it is this ...
... ¬Tsn is provable for all n is that we have a uniform proof, i.e., a proof for variable n. Moreover, no finite reasoner ever really applies the ω-rule. The only way that they can know that there is a proof of each α(i) is because they have a uniform method of constructing such proofs. And it is this ...
Document
... the truth, and knaves, who always lie. You go to the island and meet A and B. A says “B is a knight.” B says “The two of us are of opposite types.” 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 re ...
... the truth, and knaves, who always lie. You go to the island and meet A and B. A says “B is a knight.” B says “The two of us are of opposite types.” 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 re ...
Aristotle`s work on logic.
... The s-rules don’t change the copula, so if M has two negative premises, then so does si (M ). The superaltern of a negative proposition is negative and the superaltern of a positive proposition is positive. Therefore, if M has two negative premises, then so does pi (M ). The m-rule and the per-rules ...
... The s-rules don’t change the copula, so if M has two negative premises, then so does si (M ). The superaltern of a negative proposition is negative and the superaltern of a positive proposition is positive. Therefore, if M has two negative premises, then so does pi (M ). The m-rule and the per-rules ...
Aristotle, Boole, and Categories
... valid syllogism. In conjunction with any of the four figures, there are therefore 24 × 4 = 96 candidate forms, call these presyllogisms. It follows that a valid syllogism must have at least one universal premise. Furthermore if it has a particular premise then the conclusion must also be particular, ...
... valid syllogism. In conjunction with any of the four figures, there are therefore 24 × 4 = 96 candidate forms, call these presyllogisms. It follows that a valid syllogism must have at least one universal premise. Furthermore if it has a particular premise then the conclusion must also be particular, ...
Quantifiers
... some UD is truth-functionally invalid, then the original argument is FO invalid, but if it is truth-functionally valid, then that does not mean that the original argument is FO valid. • For example, with UD = {a}, the expansion of the argument would be truth-functionally valid. In general, it is alw ...
... some UD is truth-functionally invalid, then the original argument is FO invalid, but if it is truth-functionally valid, then that does not mean that the original argument is FO valid. • For example, with UD = {a}, the expansion of the argument would be truth-functionally valid. In general, it is alw ...
x - Agus Aan
... Sentence Validity • 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 ...
... Sentence Validity • 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 ...