Chapter 12 Reasoning, Logic, and Fallacies
... • Proof: Identify the size of the sample and the size of the population, then show that the sample size is too small. Note: a formal proof would require a mathematical calculation. This is the subject of probability theory. For now, you must rely on common sense. • References: Barker: 189, Cedarblom ...
... • Proof: Identify the size of the sample and the size of the population, then show that the sample size is too small. Note: a formal proof would require a mathematical calculation. This is the subject of probability theory. For now, you must rely on common sense. • References: Barker: 189, Cedarblom ...
Syntax and Semantics of Propositional and Predicate Logic
... for which both Σ ` β and Σ ` ¬β. Both of those proofs are finite. Thus the set Σ0 of premises actually used in either of these proofs is an inconsistent finite subset of Σ. By Theorem 1.14 again, Σ0 is unsatisfiable, as claimed. ...
... for which both Σ ` β and Σ ` ¬β. Both of those proofs are finite. Thus the set Σ0 of premises actually used in either of these proofs is an inconsistent finite subset of Σ. By Theorem 1.14 again, Σ0 is unsatisfiable, as claimed. ...
IntroToLogic - Department of Computer Science
... The validity of first order logic is not decidable. (It is semi-decidable.) If a theorem is logically entailed by an axiom, you can prove that it is. But if it is not, you can’t necessarily prove that it is not. (You may go on infinitely with your ...
... The validity of first order logic is not decidable. (It is semi-decidable.) If a theorem is logically entailed by an axiom, you can prove that it is. But if it is not, you can’t necessarily prove that it is not. (You may go on infinitely with your ...
Mathematical Logic Deciding logical consequence Complexity of
... Therefore, Socrates is mortal. The validity of this proof is independent of the meaning of “men”, “mortal” and “Socrates”. Indeed, even a nonsense substitution gives a valid sentence: Suppose all borogroves are mimsy. Suppose a mome rath is a borogrove. Therefore, a mome rath is mimsy. ...
... Therefore, Socrates is mortal. The validity of this proof is independent of the meaning of “men”, “mortal” and “Socrates”. Indeed, even a nonsense substitution gives a valid sentence: Suppose all borogroves are mimsy. Suppose a mome rath is a borogrove. Therefore, a mome rath is mimsy. ...
Two Marks with Answer: all units 1. Describe the Four Categories
... A Bayesian Network (Or A Belief Network) Is A Directed Acyclic Graph Which Represents Independencies Embodied In A Given Joint Probability Distribution Over A Set Of Variables. Nodes Can Represent Any Kind Of Variable, Be It A Measured Parameter, A Latent Variable Or A Hypothesis. They Are Not Restr ...
... A Bayesian Network (Or A Belief Network) Is A Directed Acyclic Graph Which Represents Independencies Embodied In A Given Joint Probability Distribution Over A Set Of Variables. Nodes Can Represent Any Kind Of Variable, Be It A Measured Parameter, A Latent Variable Or A Hypothesis. They Are Not Restr ...
Exam-Computational_Logic-Subjects_2016
... 1. Using a proof method: a) semantic method (truth table, semantic tableau, conjunctive normal form) b) syntactic method (resolution, definition of deduction, the theorem of deduction and its reverse) c) direct method (truth table, conjunctive normal form, definition of deduction, the theorem of ded ...
... 1. Using a proof method: a) semantic method (truth table, semantic tableau, conjunctive normal form) b) syntactic method (resolution, definition of deduction, the theorem of deduction and its reverse) c) direct method (truth table, conjunctive normal form, definition of deduction, the theorem of ded ...
completeness theorem for a first order linear
... temporal logics. For example, some kinds of such logics with F and P operators over various classes of time ows were axiomatized in [9], while axiomatic systems for the rst order temporal logics with since and until over linear time and rationals were given in [16]. In the case of FOLTL (and simil ...
... temporal logics. For example, some kinds of such logics with F and P operators over various classes of time ows were axiomatized in [9], while axiomatic systems for the rst order temporal logics with since and until over linear time and rationals were given in [16]. In the case of FOLTL (and simil ...
Logic - Decision Procedures
... (3) I have not filed any of them that I can read; (4) None of them, that are written on one sheet, are undated; (5) All of them, that are not crossed, are in black ink; (6) All of them, written by Brown, begin with "Dear Sir"; (7) All of them, written on blue paper, are filed; (8) None of them, writ ...
... (3) I have not filed any of them that I can read; (4) None of them, that are written on one sheet, are undated; (5) All of them, that are not crossed, are in black ink; (6) All of them, written by Brown, begin with "Dear Sir"; (7) All of them, written on blue paper, are filed; (8) None of them, writ ...
2.1-2.3: Reasoning in Geometry
... Definition of a Vehicle “Anything that has wheels and moves people from place to place.” Not all definitions may be precise, so when creating or following one, read carefully! ...
... Definition of a Vehicle “Anything that has wheels and moves people from place to place.” Not all definitions may be precise, so when creating or following one, read carefully! ...
What is Logic?
... Not logically valid, BUT can still be useful. In fact, it models the way humans reason all the time: Every non-flying bird I’ve seen before has been a penguin; hence that non-flying bird must be a penguin. ...
... Not logically valid, BUT can still be useful. In fact, it models the way humans reason all the time: Every non-flying bird I’ve seen before has been a penguin; hence that non-flying bird must be a penguin. ...
Chapter 7 Propositional and Predicate Logic
... Not logically valid, BUT can still be useful. In fact, it models the way humans reason all the time: Every non-flying bird I’ve seen before has been a penguin; hence that non-flying bird must be a penguin. ...
... Not logically valid, BUT can still be useful. In fact, it models the way humans reason all the time: Every non-flying bird I’ve seen before has been a penguin; hence that non-flying bird must be a penguin. ...
Chapter 9 Not Knowing Mar. `10 “Ignorance is the necessary
... demanding that his opponent have a better case than his own but also that the case be made known to him. If this requirement is not met, then the strategist has made his case and his opponent has failed to make him aware of a better. Hence – with misleading compactness – the strategist’s complaint: ...
... demanding that his opponent have a better case than his own but also that the case be made known to him. If this requirement is not met, then the strategist has made his case and his opponent has failed to make him aware of a better. Hence – with misleading compactness – the strategist’s complaint: ...
ppt
... A Proof System • A proof system is a syntactic system for finding formulas implied by the hypotheses – “syntactic” means manipulating syntax • i.e. manipulating formulas rather than models. – P1P2 … PnQ is a tautology ...
... A Proof System • A proof system is a syntactic system for finding formulas implied by the hypotheses – “syntactic” means manipulating syntax • i.e. manipulating formulas rather than models. – P1P2 … PnQ is a tautology ...
Definition - Rogelio Davila
... Definition. A set of wffs is consistent, sound, or satisfiable, if all their elements admit the same model. Otherwise it is said to be inconsistent. Definition. Let be a set of wffs and a wff, we say that entails , or that is a logical consequence of , , iff every model of is a mode ...
... Definition. A set of wffs is consistent, sound, or satisfiable, if all their elements admit the same model. Otherwise it is said to be inconsistent. Definition. Let be a set of wffs and a wff, we say that entails , or that is a logical consequence of , , iff every model of is a mode ...
handout - Homepages of UvA/FNWI staff
... We can make sure that the conclusion χ is not used as the major premise of an elimination rule, as we will see. We want to exclude this possibility and define a normal derivation for the full fragment as follows. Definition 2.1. A derivation is normal if every major premise of an elimination rule is ...
... We can make sure that the conclusion χ is not used as the major premise of an elimination rule, as we will see. We want to exclude this possibility and define a normal derivation for the full fragment as follows. Definition 2.1. A derivation is normal if every major premise of an elimination rule is ...
Notes Predicate Logic II
... We mentioned in “Semantics of Predicate Logic” that equality is usually interpreted to mean identity, which means that in a model a =M b holds if and only if a and b are the same elements of the model’s universe. It is safe to assume t = t for any term t, because both sides of the equation will eval ...
... We mentioned in “Semantics of Predicate Logic” that equality is usually interpreted to mean identity, which means that in a model a =M b holds if and only if a and b are the same elements of the model’s universe. It is safe to assume t = t for any term t, because both sides of the equation will eval ...
deductive system
... Some Major Formulations of Deductive Systems in Logic Let us fix a language L (of well-formed formulas). There are four main formulations of deductive systems: • Hilbert system, or axiom system: in this formulation, axioms are the main ingredient, and there are only one or two rules of inference (m ...
... Some Major Formulations of Deductive Systems in Logic Let us fix a language L (of well-formed formulas). There are four main formulations of deductive systems: • Hilbert system, or axiom system: in this formulation, axioms are the main ingredient, and there are only one or two rules of inference (m ...
Probabilistic Propositional Logic
... any probabilistic query over a set of discrete variables. • We will recognize that the hardest part here is not the cost of inference (which is really only O(2n) –no worse than the (deterministic) prop logic • The real problem is assessing probabilities. – You could need as many as 2n numbers (if al ...
... any probabilistic query over a set of discrete variables. • We will recognize that the hardest part here is not the cost of inference (which is really only O(2n) –no worse than the (deterministic) prop logic • The real problem is assessing probabilities. – You could need as many as 2n numbers (if al ...
Lesson 3
... Complete elementary disjunction (CED) of a given set S of elementary propositional symbols is an elementary disjunction in which each symbol (element of S) occurs just once: Ex.: p q Disjunctive normal form (DNF) of a formula F is a formula F’ such that F’ is equivalent to F and F’ has the form o ...
... Complete elementary disjunction (CED) of a given set S of elementary propositional symbols is an elementary disjunction in which each symbol (element of S) occurs just once: Ex.: p q Disjunctive normal form (DNF) of a formula F is a formula F’ such that F’ is equivalent to F and F’ has the form o ...
(p q r) (p q r) (p q r) (p q r) ( p q r)
... Ex.: p q Complete elementary disjunction (CED) of a given set S of elementary propositional symbols is an elementary disjunction in which each symbol (element of S) occurs just once: Ex.: p q Disjunctive normal form (DNF) of a formula F is a formula F’ such that F’ is equivalent to F and F’ ha ...
... Ex.: p q Complete elementary disjunction (CED) of a given set S of elementary propositional symbols is an elementary disjunction in which each symbol (element of S) occurs just once: Ex.: p q Disjunctive normal form (DNF) of a formula F is a formula F’ such that F’ is equivalent to F and F’ ha ...
Propositional Logic First Order Logic
... Brief historical notes on logic Propositional Logic :Syntax Propositional Logic :Semantics Satisfiability and validity Normal forms Deductive proofs and resolution Modeling with Propositional logic ...
... Brief historical notes on logic Propositional Logic :Syntax Propositional Logic :Semantics Satisfiability and validity Normal forms Deductive proofs and resolution Modeling with Propositional logic ...
Homework 8 and Sample Test
... 1. (p → p) is a tautology because a. it is intuitively obvious. b. it is not necessarily false. c. every line of it’s truth table is true. d. most people would agree with it. 2. ¬(p & ¬q) is logically equivalent to a. (p v q) b. (¬p v ¬¬q) c. (¬q v ¬p) d. (¬p → q) 3. P & P is logically equivalent to ...
... 1. (p → p) is a tautology because a. it is intuitively obvious. b. it is not necessarily false. c. every line of it’s truth table is true. d. most people would agree with it. 2. ¬(p & ¬q) is logically equivalent to a. (p v q) b. (¬p v ¬¬q) c. (¬q v ¬p) d. (¬p → q) 3. P & P is logically equivalent to ...
Yakir-Vizel-Lecture1-Intro_to_SMT
... • The Decision Problem for a given formula j is to determine whether j is valid • So clearly, a Decision Procedure… –We want it to be Sound and Complete • Sound = returns “Valid” when j is valid • Complete = terminates, and when j is valid, it returns ...
... • The Decision Problem for a given formula j is to determine whether j is valid • So clearly, a Decision Procedure… –We want it to be Sound and Complete • Sound = returns “Valid” when j is valid • Complete = terminates, and when j is valid, it returns ...
logical axiom
... 2. (a → (b → c)) → ((a → b) → (a → c)) 3. (¬a → ¬b) → (b → a) where → is a binary logical connective and ¬ is a unary logical connective, and a, b, c are any (well-formed) formulas. Let us take these formulas as axioms. Next, we pick a rule of inference. The popular choice is the rule “modus ponens ...
... 2. (a → (b → c)) → ((a → b) → (a → c)) 3. (¬a → ¬b) → (b → a) where → is a binary logical connective and ¬ is a unary logical connective, and a, b, c are any (well-formed) formulas. Let us take these formulas as axioms. Next, we pick a rule of inference. The popular choice is the rule “modus ponens ...
Full version - Villanova Computer Science
... Below are a few theses about what your lecturer believes logic is or should be: 1. Logic is the most basic, general-purpose, universal-utility tool for reasoning and acting rationally. 2. All intellectual activities (sciences, engineering, politics, everyday life) are or should be based on logic, wh ...
... Below are a few theses about what your lecturer believes logic is or should be: 1. Logic is the most basic, general-purpose, universal-utility tool for reasoning and acting rationally. 2. All intellectual activities (sciences, engineering, politics, everyday life) are or should be based on logic, wh ...