Inference in Cyc. Copyright 2002 Cycorp


 Kelley Wilkinson
 4 years ago
 Views:
Transcription
1 Inference in Cyc Logical Aspects of Inference Incompleteness in Searching Incompleteness from Resource Bounds and Continuable Searches Efficiency through Heuristics Inference Features in Cyc We ll be talking about Inference in Cyc. Inference is the mechanism we use to conclude new facts from other existing facts and rules in the system. We ll be talking about it in four sections and the first section will be about the logical aspects of inference. 1
2 Inference uses Deduction: Rules Rules  general, variables (#$mother?person?mother) (#$loves?person?mother)) Rules are very general statements in a formal logical language, such as this formula, under Rules, which essentially says that everyone loves their mother. If?MOTHER is the mother of some?person, then that?person loves that?mother. It s a conditional statement. It s general  it doesn t apply to one specific thing and it quantifies over objects in the world. As such it usually has variables (i.e.?person ) in it and there are usually multiple literals, or statements, that are connected together by logical connectives (i.e. implies ). Rules tend to be the complicated logical statements. The other statements in the system can be colloquially described as facts. 2
3 Inference uses Deduction: Facts Facts  specific, no variables, atomic (#$mother #$Hamlet #$Gertrude) Facts tend to be about some very specific thing in the world  unlike rules which are general. They tend to be ground, meaning that they don t have any variables in them, because they re talking about some specific case, they re not quantifying over the world. Facts are also atomic, which has to do with it being a single statement, like the mother of Hamlet is Gertrude. It is the application of a predicate, #$mother, to arguments, #$Hamlet and #$Gertrude. So the rule from the previous slide would not be atomic because there are two literals connected together by a logical connective to say that if this (a person has a mother) were the case, then this (a person loves their mother) would be the case. So something is atomic if there is no conditional aspect to it, if it s just a single statement. Facts are more formally called ground atomic formulas because they are formulas that are both ground and atomic. 3
4 Inference uses Deduction: Nonatomic terms, Predicates, and Functions Nonatomic terms are functional (#$BabyFn #$Jaguar) Predicates are true or false (#$mother #$Hamlet #$Gertrude) Functions denote a new term (#$BabyFn #$Jaguar) A nonatomic term would be a functional term, something like (#$BabyFn #$Jaguar). Let s say you had a function called #$BabyFn that applies to any animal type and you can use it to denote the baby forms of any animal. So you could denote a baby cat, a baby whale, or a baby jaguar. There is a distinction between predicates and functions in logic. Predicates are statements about the truth of something  it is either true or it s not. In the case of (#$mother #$Hamlet #$Gertrude), it s stating it is true that the mother of Hamlet is Gertrude. Functions denote a new term that you re talking about. The application of #$BabyFn to #$Jaguar does not say it is true that BabyFn of Jaguar. That doesn t make any sense. The application of #$BabyFn to #$Jaguar allows you to denote a new concept, that of Baby Jaguar. Functions and predicates can both be used to make what Cyc calls formulas. 4
5 Inference uses Deduction: Formulas and Logic Formula  a relation applied to arguments (#$mother?person?mother) (#$loves?person?mother)) Cyc s Inference uses standard logical deductions All men are mortal. Socrates is a man. Socrates is mortal. A formula is just an operator applied to arguments. In that sense, logical connectives like #$implies, #$and, and #$or are also operators. So the previous example of a rule is a formula as well. The operator #$implies takes two formulas as arguments and maks a larger formula. This is what a logical connective is  it is something that connects formulas into more complex formulas. The basis for inference in Cyc is just performing the standard logical deductions or syllogisms that you learn in logic classes: All men are mortal. Socrates is a man. Therefore, Socrates is mortal. This is just to point out that the basis of our system is not Bayesian Reasoning or fuzzy logic or something like that. For every inference step we make, we actually have a logicallysound proof behind it that you can look at to see X is true specifically because I did a deduction and Y and Z are the two things which together allow me to conclude it. This will be important later, when we describe how we perform truth maintenance in our system. 5
6 Inference uses Deduction: Rules + Facts Deduction  rule + fact(s) => new fact (#$loves #$Hamlet #$Gertrude) Rules  general, variables (#$mother?person?mother) (#$loves?person?mother)) Facts  specific, no variables (#$mother #$Hamlet #$Gertrude) Our system uses logical deduction as the basis for inference. This can be tersely summarized as the application of rules plus facts to conclude some new facts. An example of a fact is the mother of Hamlet is Gertrude. You can use this fact plus the rule from previous slides to perform a logical deduction. This deductive inference would be that because of this rule (everyone loves their mother) and this fact (the mother of Hamlet is Gertrude) you can logically conclude that Hamlet loves Gertrude. 6
7 The Resolution Principle Resolution Principle : Unify, Substitute, Merge Query Rule (#$mother?person?mother) (#$loves?person?mother)) Let s talk in a little more detail about how we perform these logical deductions. The specific method that we use is the Resolution Principle. The Resolution Principle is a very standard logical mechanism for connecting two logical statements to come up with a third one. The algorithm that embodies the resolution principle can be tersely summarized as Unify, Substitute, and Merge, in that order. I ll describe each of these steps in this next example. Assume for a moment that I have a question that I m asking the system: Who is it that Hamlet both knows and loves? I want the system to try and prove what answers for Who? are in our system. So, given that the formula on the left of the slide is the query that I m asking, and we have the rule on the right of the slide in our system (which says that everyone loves their mother), then one way of concluding who someone loves would be if you know who their mother is. 7
8 The Resolution Principle: Unify Resolution Principle : Unify, Substitute, Merge Query Rule (#$mother?person?mother) (#$loves?person?mother)) Pivot Literals I can use the query and the rule to perform one logical deductive step: I can prove an answer for your query if I can prove an answer for something else because of some rule in the system. In effect, an application of the Resolution Principle allows you to take one logical formula and use it in concert with the thing you re trying to prove to help you turn it into something else you should try and prove. This can either be more complicated or less complicated than what you start with. I ll talk about the ramifications of both of those options later. For now, let s look at how we would perform this one step in this case. The act of combining the query and the rule to help answer part of the query is one deductive step. The following is how we apply the resolution principle to this situation. The key is to identify one particular literal which is common between the two. In this case, we have the literal Who does Hamlet love? and a rule that would allow us to conclude who everyone loves. Who does Hamlet love? would be called the pivot literal in the query and Person loves its mother would be called the pivot literal in the rule because these are the literals around which the whole step pivots. So we identify that we are going to try and prove this literal, (#$loves #$Hamlet?WHO), using the rule on the right of the slide. 8
9 The Resolution Principle: Unify Resolution Principle : Unify, Substitute, Merge Query Rule (#$mother?person?mother) (#$loves?person?mother)) Most General Unifier #$Hamlet /?PERSON?WHO /?MOTHER = Se we have decided to see if we can prove the loves part, the third line of the query, using the third line of the rule. We can do it by unifying the loves from the query with the loves from the rule. The unification step is attempting to identify a way of making the two loves literals exactly the same. This is the essence of Unification. We re trying to come up with a recipe for how to make both of these actually exactly the same. That recipe is referred to as the Most General Unifier. This is a recipe for substituting one thing for another such that if you did the substitution, then you would actually have the exact same thing. So, in this case, we can get the literals to be exactly the same with this proviso: if #$Hamlet is matched up with?person and?who is matched up with?mother. It s called the Most General Unifier because we make the most conservative recipe possible  we re not committing to anything more than we have to in order to get these things to match and that makes it most general. So once we ve identified the Most General Unifier, the most general recipe for making them the same, we ve completed the unifying step. 9
10 The Resolution Principle: Substitute Resolution Principle : Unify, Substitute, Merge Query Most General Unifier #$Hamlet /?PERSON?WHO /?MOTHER Rule (#$mother?person?mother) (#$loves?person?mother)) Substituted Query Substituted Rule (#$mother #$Hamlet?WHO) Given the Most General Unifier, we can apply this recipe to both of them to perform the Substitution step. We apply this recipe to one literal in order to get it to be the same as the other. If I substitute into the rule, #$Hamlet for?person and?who for?mother, I ll then have something in which the third line of both the query and the rule exactly match. We also apply the Most General Unifier to the rest of the query and the rule. This is a simple unification, but it is common in the inference that Cyc normally does. 10
11 The Resolution Principle: Merge Resolution Principle : Unify, Substitute, Merge Substituted Query Substituted Rule (#$mother #$Hamlet?WHO) (#$loves?hamlet?who)) Merged Query (#$mother #$Hamlet?WHO)) The final step is the Merge step, where we then take the remaining pieces of both and merge them together into something like what you see at the bottom of the slide. The loves part disappears because that s the thing that actually got proved in this step. The result of the merge is a combination of the two substituted pieces together. So, we start out with Who does Hamlet know and love? and using this rule, Everyone loves their mother, we can turn our original query into Who does Hamlet know? And is that person Hamlet s mother? If I were to find an answer for the new, merged question, then because of the rule, it would be an answer for the query. So what results is a new thing, shown at the bottom of the slide, that we try and prove. It indicates that any answer for the formula, because of the rule on the right of the slide, would be an answer for the query on the left of the slide. 11
12 The Resolution Principle using a fact Query Resolution Principle : Unify, Substitute, Merge Fact (#$loves #$Hamlet #$Ophelia) Most General Unifier?WHO / #$Ophelia (#$knows #$Hamlet #$Ophelia) So, the act of inference is taking things that you're trying to prove and applying things you already know in order to find different things to prove. Hopefully these things you are trying to prove eventually reduce down to something like true which is patently true already and does not need to be proven. Therefore, the path of how you got there would provide one complete logical proof of an answer. Let s look at another example of the Resolution Principle  one that uses a fact instead of a rule. Let s say that we actually have Hamlet loves Ophelia as a fact instead of a rule. We re still asking Who does Hamlet know and love? I can use the fact Hamlet loves Ophelia to resolve against the loves literal in the query. In this case, the Most General Unifier would be simpler. It would just be matching?who with #$Ophelia. All that would be left to prove is if Hamlet knows Ophelia, so down below we have a very simple statement. This would usually be proved using some other knowledge, for example Ophelia is Hamlet s friend and everyone knows their friends, or something like that. With this, I could reduce the formula (#$knows #$Hamlet #$Ophelia) down to #$True. There would be nothing left to prove. It would be like there being an empty degenerate ) in the query, which is equivalent to #$True. This example shows that the use of a fact strictly simplifies a proof, while the use of a rule usually leaves a proof at least as complicated and sometimes more complicated (if it has more conditions in the antecedent) than the original. 12
13 Resolving to #$True Query Rule Most General Unifier New Query Hamlet knows and loves Ophelia. New Query Rule Most General Unifier Newer Query Newer Query Rule Most General Unifier Newest Query Newest Query Fact Most General Unifier #$True #$True => the end Let me say more about proving True. Once you arrive at #$True as the final thing to prove, you can realize that #$True is true, so you ve actually finally proved it  you ve reached the end. This leaves you with one complete deductive proof such that you can walk backwards and say What did I use in each step along the way? and collect up the formulas that you used along the way to make each step. By collecting all of the Most General Unifiers involved in the proof, you can see things like what did this variable?who get bound to? Oh, it eventually got bound to #$Ophelia here. So this kind of information keeps getting passed up to the top and eventually out the top will bubble an answer. Here is one answer for what you asked for and the path all the way down has each step along the way  the intermediate steps (Most General Unifiers) and how you proved them, and what you used to justify this answer. Next we ll be talking about how we actually algorithmically perform all of these resolution steps. We just described logically how Cyc performs inference and in the next lesson we re going to describe in more detail the mechanism that we use to perform these logical deductions. 13
14 Summary Inference uses Deduction Facts + Rules => New Fact Rules vs. Facts Predicates vs. Functions Inference uses Resolution The Resolution Principle: Unify, Substitute, Merge Resolving to #$True This concludes the lesson on the logical aspects of Inference. 14
Artificial Intelligence Prof. P. Dasgupta Department of Computer Science & Engineering Indian Institute of Technology, Kharagpur
Artificial Intelligence Prof. P. Dasgupta Department of Computer Science & Engineering Indian Institute of Technology, Kharagpur Lecture 10 Inference in First Order Logic I had introduced first order
More informationInference in Cyc. This is the final lesson in the Inference Tutorial. It will focus on microtheories and forward/backward inference.
Inference in Cyc Logical Aspects of Inference Incompleteness in Searching Incompleteness from Resource Bounds and Continuable Searches Efficiency through Heuristics Inference Features in Cyc This is the
More informationRevisiting the Socrates Example
Section 1.6 Section Summary Valid Arguments Inference Rules for Propositional Logic Using Rules of Inference to Build Arguments Rules of Inference for Quantified Statements Building Arguments for Quantified
More informationArtificial Intelligence: Valid Arguments and Proof Systems. Prof. Deepak Khemani. Department of Computer Science and Engineering
Artificial Intelligence: Valid Arguments and Proof Systems Prof. Deepak Khemani Department of Computer Science and Engineering Indian Institute of Technology, Madras Module 02 Lecture  03 So in the last
More information(Refer Slide Time 03:00)
Artificial Intelligence Prof. Anupam Basu Department of Computer Science and Engineering Indian Institute of Technology, Kharagpur Lecture  15 Resolution in FOPL In the last lecture we had discussed about
More informationArtificial Intelligence. Clause Form and The Resolution Rule. Prof. Deepak Khemani. Department of Computer Science and Engineering
Artificial Intelligence Clause Form and The Resolution Rule Prof. Deepak Khemani Department of Computer Science and Engineering Indian Institute of Technology, Madras Module 07 Lecture 03 Okay so we are
More informationSemantic Entailment and Natural Deduction
Semantic Entailment and Natural Deduction Alice Gao Lecture 6, September 26, 2017 Entailment 1/55 Learning goals Semantic entailment Define semantic entailment. Explain subtleties of semantic entailment.
More informationAnnouncements. CS243: Discrete Structures. First Order Logic, Rules of Inference. Review of Last Lecture. Translating English into FirstOrder Logic
Announcements CS243: Discrete Structures First Order Logic, Rules of Inference Işıl Dillig Homework 1 is due now Homework 2 is handed out today Homework 2 is due next Tuesday Işıl Dillig, CS243: Discrete
More informationIn this section you will learn three basic aspects of logic. When you are done, you will understand the following:
Basic Principles of Deductive Logic Part One: In this section you will learn three basic aspects of logic. When you are done, you will understand the following: Mental Act Simple Apprehension Judgment
More informationArtificial Intelligence Prof. P. Dasgupta Department of Computer Science & Engineering Indian Institute of Technology, Kharagpur
Artificial Intelligence Prof. P. Dasgupta Department of Computer Science & Engineering Indian Institute of Technology, Kharagpur Lecture 9 First Order Logic In the last class, we had seen we have studied
More informationA BRIEF INTRODUCTION TO LOGIC FOR METAPHYSICIANS
A BRIEF INTRODUCTION TO LOGIC FOR METAPHYSICIANS 0. Logic, Probability, and Formal Structure Logic is often divided into two distinct areas, inductive logic and deductive logic. Inductive logic is concerned
More informationReasoning and DecisionMaking under Uncertainty
Reasoning and DecisionMaking under Uncertainty 3. Termin: Uncertainty, Degrees of Belief and Probabilities Prof. Dr.Ing. Stefan Kopp Center of Excellence Cognitive Interaction Technology AG A Intelligent
More informationRussell on Denoting. G. J. Mattey. Fall, 2005 / Philosophy 156. The concept any finite number is not odd, nor is it even.
Russell on Denoting G. J. Mattey Fall, 2005 / Philosophy 156 Denoting in The Principles of Mathematics This notion [denoting] lies at the bottom (I think) of all theories of substance, of the subjectpredicate
More informationDay 3. Wednesday May 23, Learn the basic building blocks of proofs (specifically, direct proofs)
Day 3 Wednesday May 23, 2012 Objectives: Learn the basics of Propositional Logic Learn the basic building blocks of proofs (specifically, direct proofs) 1 Propositional Logic Today we introduce the concepts
More informationINTERMEDIATE LOGIC Glossary of key terms
1 GLOSSARY INTERMEDIATE LOGIC BY JAMES B. NANCE INTERMEDIATE LOGIC Glossary of key terms This glossary includes terms that are defined in the text in the lesson and on the page noted. It does not include
More informationSelections from Aristotle s Prior Analytics 41a21 41b5
Lesson Seventeen The Conditional Syllogism Selections from Aristotle s Prior Analytics 41a21 41b5 It is clear then that the ostensive syllogisms are effected by means of the aforesaid figures; these considerations
More informationLogicola Truth Evaluation Exercises
Logicola Truth Evaluation Exercises The Logicola exercises for Ch. 6.3 concern truth evaluations, and in 6.4 this complicated to include unknown evaluations. I wanted to say a couple of things for those
More informationAnnouncements. CS311H: Discrete Mathematics. First Order Logic, Rules of Inference. Satisfiability, Validity in FOL. Example.
Announcements CS311H: Discrete Mathematics First Order Logic, Rules of Inference Instructor: Işıl Dillig Homework 1 is due now! Homework 2 is handed out today Homework 2 is due next Wednesday Instructor:
More informationA. Problem set #3 it has been posted and is due Tuesday, 15 November
Lecture 9: Propositional Logic I Philosophy 130 1 & 3 November 2016 O Rourke & Gibson I. Administrative A. Problem set #3 it has been posted and is due Tuesday, 15 November B. I am working on the group
More informationBasic Concepts and Skills!
Basic Concepts and Skills! Critical Thinking tests rationales,! i.e., reasons connected to conclusions by justifying or explaining principles! Why do CT?! Answer: Opinions without logical or evidential
More information10.3 Universal and Existential Quantifiers
M10_COPI1396_13_SE_C10.QXD 10/22/07 8:42 AM Page 441 10.3 Universal and Existential Quantifiers 441 and Wx, and so on. We call these propositional functions simple predicates, to distinguish them from
More informationChapter 6, Tutorial 1 Predicate Logic Introduction
Chapter 6, Tutorial 1 Predicate Logic Introduction In this chapter, we extend our formal language beyond sentence letters and connectives. And even beyond predicates and names. Just one small wrinkle,
More informationAlso, in Argument #1 (Lecture 11, Slide 11), the inference from steps 2 and 3 to 4 is stated as:
by SALVATORE  5 September 2009, 10:44 PM I`m having difficulty understanding what steps to take in applying valid argument forms to do a proof. What determines which given premises one should select to
More informationWhat would count as Ibn Sīnā (11th century Persia) having first order logic?
1 2 What would count as Ibn Sīnā (11th century Persia) having first order logic? Wilfrid Hodges Herons Brook, Sticklepath, Okehampton March 2012 http://wilfridhodges.co.uk Ibn Sina, 980 1037 3 4 Ibn Sīnā
More informationHANDBOOK (New or substantially modified material appears in boxes.)
1 HANDBOOK (New or substantially modified material appears in boxes.) I. ARGUMENT RECOGNITION Important Concepts An argument is a unit of reasoning that attempts to prove that a certain idea is true by
More informationModule 5. Knowledge Representation and Logic (Propositional Logic) Version 2 CSE IIT, Kharagpur
Module 5 Knowledge Representation and Logic (Propositional Logic) Lesson 12 Propositional Logic inference rules 5.5 Rules of Inference Here are some examples of sound rules of inference. Each can be shown
More informationHANDBOOK (New or substantially modified material appears in boxes.)
1 HANDBOOK (New or substantially modified material appears in boxes.) I. ARGUMENT RECOGNITION Important Concepts An argument is a unit of reasoning that attempts to prove that a certain idea is true by
More informationPearson Education Limited Edinburgh Gate Harlow Essex CM20 2JE England and Associated Companies throughout the world
Pearson Education Limited Edinburgh Gate Harlow Essex CM20 2JE England and Associated Companies throughout the world Visit us on the World Wide Web at: www.pearsoned.co.uk Pearson Education Limited 2014
More informationHANDBOOK. IV. Argument Construction Determine the Ultimate Conclusion Construct the Chain of Reasoning Communicate the Argument 13
1 HANDBOOK TABLE OF CONTENTS I. Argument Recognition 2 II. Argument Analysis 3 1. Identify Important Ideas 3 2. Identify Argumentative Role of These Ideas 4 3. Identify Inferences 5 4. Reconstruct the
More informationBertrand Russell Proper Names, Adjectives and Verbs 1
Bertrand Russell Proper Names, Adjectives and Verbs 1 Analysis 46 Philosophical grammar can shed light on philosophical questions. Grammatical differences can be used as a source of discovery and a guide
More informationSemantic Foundations for Deductive Methods
Semantic Foundations for Deductive Methods delineating the scope of deductive reason Roger Bishop Jones Abstract. The scope of deductive reason is considered. First a connection is discussed between the
More informationVenn Diagrams and Categorical Syllogisms. Unit 5
Venn Diagrams and Categorical Syllogisms Unit 5 John Venn 1834 1923 English logician and philosopher noted for introducing the Venn diagram Used in set theory, probability, logic, statistics, and computer
More information16. Universal derivation
16. Universal derivation 16.1 An example: the Meno In one of Plato s dialogues, the Meno, Socrates uses questions and prompts to direct a young slave boy to see that if we want to make a square that has
More informationVerification and Validation
20122013 Verification and Validation Part III : Proofbased Verification Burkhart Wolff Département Informatique Université ParisSud / Orsay " Now, can we build a Logic for Programs??? 05/11/14 B. Wolff
More informationEarly Russell on Philosophical Grammar
Early Russell on Philosophical Grammar G. J. Mattey Fall, 2005 / Philosophy 156 Philosophical Grammar The study of grammar, in my opinion, is capable of throwing far more light on philosophical questions
More informationA Note on StraightThinking
A Note on StraightThinking A supplementary note for the 2nd Annual JTS/CGST Public Ethics Lecture March 5, 2002(b), adj. 2009:03:05 G.E.M. of TKI Arguments & Appeals In arguments, people try to persuade
More information(1) A phrase may be denoting, and yet not denote anything; e.g., 'the present King of France'.
On Denoting By Russell Based on the 1903 article By a 'denoting phrase' I mean a phrase such as any one of the following: a man, some man, any man, every man, all men, the present King of England, the
More information2.1 Review. 2.2 Inference and justifications
Applied Logic Lecture 2: Evidence Semantics for Intuitionistic Propositional Logic Formal logic and evidence CS 4860 Fall 2012 Tuesday, August 28, 2012 2.1 Review The purpose of logic is to make reasoning
More informationLogic & Proofs. Chapter 3 Content. Sentential Logic Semantics. Contents: Studying this chapter will enable you to:
Sentential Logic Semantics Contents: TruthValue Assignments and TruthFunctions TruthValue Assignments TruthFunctions Introduction to the TruthLab TruthDefinition Logical Notions TruthTrees Studying
More informationCHAPTER 1 A PROPOSITIONAL THEORY OF ASSERTIVE ILLOCUTIONARY ARGUMENTS OCTOBER 2017
CHAPTER 1 A PROPOSITIONAL THEORY OF ASSERTIVE ILLOCUTIONARY ARGUMENTS OCTOBER 2017 Man possesses the capacity of constructing languages, in which every sense can be expressed, without having an idea how
More informationFoundations of Knowledge Representation in Cyc
Foundations of Knowledge Representation in Cyc Why use logic? CycL Syntax Collections and Individuals (#$isa and #$) Microtheories This section is a continuation of the tutorial on foundations of knowledge
More informationLogic: The Science that Evaluates Arguments
Logic: The Science that Evaluates Arguments Logic teaches us to develop a system of methods and principles to use as criteria for evaluating the arguments of others to guide us in constructing arguments
More information2.3. Failed proofs and counterexamples
2.3. Failed proofs and counterexamples 2.3.0. Overview Derivations can also be used to tell when a claim of entailment does not follow from the principles for conjunction. 2.3.1. When enough is enough
More information6.080 / Great Ideas in Theoretical Computer Science Spring 2008
MIT OpenCourseWare http://ocw.mit.edu 6.080 / 6.089 Great Ideas in Theoretical Computer Science Spring 2008 For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms.
More informationTransition to Quantified Predicate Logic
Transition to Quantified Predicate Logic Predicates You may remember (but of course you do!) during the first class period, I introduced the notion of validity with an argument much like (with the same
More informationAn Introduction to. Formal Logic. Second edition. Peter Smith, February 27, 2019
An Introduction to Formal Logic Second edition Peter Smith February 27, 2019 Peter Smith 2018. Not for reposting or recirculation. Comments and corrections please to ps218 at cam dot ac dot uk 1 What
More informationCONTENTS A SYSTEM OF LOGIC
EDITOR'S INTRODUCTION NOTE ON THE TEXT. SELECTED BIBLIOGRAPHY XV xlix I /' ~, r ' o>
More informationChapter 9 Sentential Proofs
Logic: A Brief Introduction Ronald L. Hall, Stetson University Chapter 9 Sentential roofs 9.1 Introduction So far we have introduced three ways of assessing the validity of truthfunctional arguments.
More informationHOW TO ANALYZE AN ARGUMENT
What does it mean to provide an argument for a statement? To provide an argument for a statement is an activity we carry out both in our everyday lives and within the sciences. We provide arguments for
More informationRussell: On Denoting
Russell: On Denoting DENOTING PHRASES Russell includes all kinds of quantified subject phrases ( a man, every man, some man etc.) but his main interest is in definite descriptions: the present King of
More informationlogic is everywhere Logik ist überall Hikmat har Jaga Hai Mantık her yerde la logica è dappertutto lógica está em toda parte
SHRUTI and Reflexive Reasoning Steffen Hölldobler logika je všude International Center for Computational Logic Technische Universität Dresden Germany logic is everywhere FirstOrder Logic la lógica está
More informationChapter 8  Sentential Truth Tables and Argument Forms
Logic: A Brief Introduction Ronald L. Hall Stetson University Chapter 8  Sentential ruth ables and Argument orms 8.1 Introduction he truthvalue of a given truthfunctional compound proposition depends
More informationPart II: How to Evaluate Deductive Arguments
Part II: How to Evaluate Deductive Arguments Week 4: Propositional Logic and Truth Tables Lecture 4.1: Introduction to deductive logic Deductive arguments = presented as being valid, and successful only
More informationSOME RADICAL CONSEQUENCES OF GEACH'S LOGICAL THEORIES
SOME RADICAL CONSEQUENCES OF GEACH'S LOGICAL THEORIES By james CAIN ETER Geach's views of relative identity, together with his Paccount of proper names and quantifiers, 1 while presenting what I believe
More informationSuppressed premises in real life. Philosophy and Logic Section 4.3 & Some Exercises
Suppressed premises in real life Philosophy and Logic Section 4.3 & Some Exercises Analyzing inferences: finale Suppressed premises: from mechanical solutions to elegant ones Practicing on some reallife
More informationA Model of Decidable Introspective Reasoning with QuantifyingIn
A Model of Decidable Introspective Reasoning with QuantifyingIn Gerhard Lakemeyer* Institut fur Informatik III Universitat Bonn Romerstr. 164 W5300 Bonn 1, Germany email: gerhard@uran.informatik.unibonn,de
More informationUC Berkeley, Philosophy 142, Spring 2016
Logical Consequence UC Berkeley, Philosophy 142, Spring 2016 John MacFarlane 1 Intuitive characterizations of consequence Modal: It is necessary (or apriori) that, if the premises are true, the conclusion
More informationMoore on External Relations
Moore on External Relations G. J. Mattey Fall, 2005 / Philosophy 156 The Dogma of Internal Relations Moore claims that there is a dogma held by philosophers such as Bradley and Joachim, that all relations
More informationLogic: Deductive and Inductive by Carveth Read M.A. CHAPTER VI CONDITIONS OF IMMEDIATE INFERENCE
CHAPTER VI CONDITIONS OF IMMEDIATE INFERENCE Section 1. The word Inference is used in two different senses, which are often confused but should be carefully distinguished. In the first sense, it means
More informationLogic for Computer Science  Week 1 Introduction to Informal Logic
Logic for Computer Science  Week 1 Introduction to Informal Logic Ștefan Ciobâcă November 30, 2017 1 Propositions A proposition is a statement that can be true or false. Propositions are sometimes called
More informationThe Development of Laws of Formal Logic of Aristotle
This paper is dedicated to my unforgettable friend Boris Isaevich Lamdon. The Development of Laws of Formal Logic of Aristotle The essence of formal logic The aim of every science is to discover the laws
More informationPhilosophy 1100: Introduction to Ethics. Critical Thinking Lecture 1. Background Material for the Exercise on Validity
Philosophy 1100: Introduction to Ethics Critical Thinking Lecture 1 Background Material for the Exercise on Validity Reasons, Arguments, and the Concept of Validity 1. The Concept of Validity Consider
More informationVan Inwagen's modal argument for incompatibilism
University of Windsor Scholarship at UWindsor Critical Reflections Essays of Significance & Critical Reflections 2015 Mar 28th, 2:00 PM  2:30 PM Van Inwagen's modal argument for incompatibilism Katerina
More informationThe SAT Essay: An ArgumentCentered Strategy
The SAT Essay: An ArgumentCentered Strategy Overview Taking an argumentcentered approach to preparing for and to writing the SAT Essay may seem like a nobrainer. After all, the prompt, which is always
More information9 Methods of Deduction
M09_COPI1396_13_SE_C09.QXD 10/19/07 3:46 AM Page 372 9 Methods of Deduction 9.1 Formal Proof of Validity 9.2 The Elementary Valid Argument Forms 9.3 Formal Proofs of Validity Exhibited 9.4 Constructing
More information6: DEDUCTIVE LOGIC. Chapter 17: Deductive validity and invalidity Ben Bayer Drafted April 25, 2010 Revised August 23, 2010
6: DEDUCTIVE LOGIC Chapter 17: Deductive validity and invalidity Ben Bayer Drafted April 25, 2010 Revised August 23, 2010 Deduction vs. induction reviewed In chapter 14, we spent a fair amount of time
More information1. Lukasiewicz s Logic
Bulletin of the Section of Logic Volume 29/3 (2000), pp. 115 124 Dale Jacquette AN INTERNAL DETERMINACY METATHEOREM FOR LUKASIEWICZ S AUSSAGENKALKÜLS Abstract An internal determinacy metatheorem is proved
More information1 Clarion Logic Notes Chapter 4
1 Clarion Logic Notes Chapter 4 Summary Notes These are summary notes so that you can really listen in class and not spend the entire time copying notes. These notes will not substitute for reading the
More information9.1 Intro to Predicate Logic Practice with symbolizations. Today s Lecture 3/30/10
9.1 Intro to Predicate Logic Practice with symbolizations Today s Lecture 3/30/10 Announcements Tests back today Homework: Ex 9.1 pgs. 431432 Part C (125) Predicate Logic Consider the argument: All
More informationModule 02 Lecture  10 Inferential Statistics Single Sample Tests
Introduction to Data Analytics Prof. Nandan Sudarsanam and Prof. B. Ravindran Department of Management Studies and Department of Computer Science and Engineering Indian Institute of Technology, Madras
More informationMathematics in and behind Russell s logicism, and its
The Cambridge companion to Bertrand Russell, edited by Nicholas Griffin, Cambridge University Press, Cambridge, UK and New York, US, xvii + 550 pp. therein: Ivor GrattanGuinness. reception. Pp. 51 83.
More informationArtificial Intelligence Prof. Deepak Khemani Department of Computer Science and Engineering Indian Institute of Technology, Madras
(Refer Slide Time: 00:26) Artificial Intelligence Prof. Deepak Khemani Department of Computer Science and Engineering Indian Institute of Technology, Madras Lecture  06 State Space Search Intro So, today
More informationOverview of Today s Lecture
Branden Fitelson Philosophy 12A Notes 1 Overview of Today s Lecture Music: Robin Trower, Daydream (King Biscuit Flower Hour concert, 1977) Administrative Stuff (lots of it) Course Website/Syllabus [i.e.,
More informationLogical (formal) fallacies
Fallacies in academic writing Chad Nilep There are many possible sources of fallacy an idea that is mistakenly thought to be true, even though it may be untrue in academic writing. The phrase logical fallacy
More informationLogic Appendix: More detailed instruction in deductive logic
Logic Appendix: More detailed instruction in deductive logic Standardizing and Diagramming In Reason and the Balance we have taken the approach of using a simple outline to standardize short arguments,
More informationQuantificational logic and empty names
Quantificational logic and empty names Andrew Bacon 26th of March 2013 1 A Puzzle For Classical Quantificational Theory Empty Names: Consider the sentence 1. There is something identical to Pegasus On
More informationStructure and essence: The keys to integrating spirituality and science
Structure and essence: The keys to integrating spirituality and science Copyright c 2001 Paul P. Budnik Jr., All rights reserved Our technical capabilities are increasing at an enormous and unprecedented
More informationPhilosophy 1100: Ethics
Philosophy 1100: Ethics Topic 1  Course Introduction: 1. What is Philosophy? 2. What is Ethics? 3. Logic a. Truth b. Arguments c. Validity d. Soundness What is Philosophy? The Three Fundamental Questions
More informationRichard Carrier, Ph.D.
Richard Carrier, Ph.D. www.richardcarrier.info LOGIC AND CRITICAL THOUGHT IN THE 21ST CENTURY What s New and Why It Matters BREAKDOWN Traditional Principles of Critical Thinking Plus a Dash of Cognitive
More informationWhat is the Frege/Russell Analysis of Quantification? Scott Soames
What is the Frege/Russell Analysis of Quantification? Scott Soames The FregeRussell analysis of quantification was a fundamental advance in semantics and philosophical logic. Abstracting away from details
More informationSearle vs. Chalmers Debate, 8/2005 with Death Monkey (Kevin Dolan)
Searle vs. Chalmers Debate, 8/2005 with Death Monkey (Kevin Dolan) : Searle says of Chalmers book, The Conscious Mind, "it is one thing to bite the occasional bullet here and there, but this book consumes
More informationAquinas, The Divine Nature
Aquinas, The Divine Nature So far we have shown THAT God exists, but we don t yet know WHAT God is like. Here, Aquinas demonstrates attributes of God, who is: (1) Simple (i.e., God has no parts) (2) Perfect
More informationAnthony P. Andres. The Place of Conversion in Aristotelian Logic. Anthony P. Andres
[ Loyola Book Comp., run.tex: 0 AQR Vol. W rev. 0, 17 Jun 2009 ] [The Aquinas Review Vol. W rev. 0: 1 The Place of Conversion in Aristotelian Logic From at least the time of John of St. Thomas, scholastic
More informationExperimental Design. Introduction
Ecologists generally, and marine biologists in particular, do not spend sufficient time, at least according to the available literature, in introspection about the nature of the science that they do Underwood
More informationLogic: Deductive and Inductive by Carveth Read M.A. CHAPTER IX CHAPTER IX FORMAL CONDITIONS OF MEDIATE INFERENCE
CHAPTER IX CHAPTER IX FORMAL CONDITIONS OF MEDIATE INFERENCE Section 1. A Mediate Inference is a proposition that depends for proof upon two or more other propositions, so connected together by one or
More informationTautological Necessity and Tautological Validity With Quantifiers
Some sentences containing quantifiers are truth table necessary. Tautological Necessity and Tautological Validity With Quantifiers Mark Criley IWU 25 October 2017 That is, they are forced to be true just
More informationSYLLOGISTIC LOGIC CATEGORICAL PROPOSITIONS
Prof. C. Byrne Dept. of Philosophy SYLLOGISTIC LOGIC Syllogistic logic is the original form in which formal logic was developed; hence it is sometimes also referred to as Aristotelian logic after Aristotle,
More information[3.] Bertrand Russell. 1
[3.] Bertrand Russell. 1 [3.1.] Biographical Background. 1872: born in the city of Trellech, in the county of Monmouthshire, now part of Wales 2 One of his grandfathers was Lord John Russell, who twice
More information1. Introduction Formal deductive logic Overview
1. Introduction 1.1. Formal deductive logic 1.1.0. Overview In this course we will study reasoning, but we will study only certain aspects of reasoning and study them only from one perspective. The special
More informationInformalizing Formal Logic
Informalizing Formal Logic Antonis Kakas Department of Computer Science, University of Cyprus, Cyprus antonis@ucy.ac.cy Abstract. This paper discusses how the basic notions of formal logic can be expressed
More informationON DENOTING BERTRAND RUSSELL ORIGINALLY PUBLISHED IN MIND 14.4 (1905): THIS COPY FROM PHILOSOPHYINDEX.COM.
ON DENOTING BERTRAND RUSSELL ORIGINALLY PUBLISHED IN MIND 14.4 (1905): 479493. THIS COPY FROM PHILOSOPHYINDEX.COM. By a denoting phrase I mean a phrase such as any one of the following: a man, some man,
More informationOutline. 1 Review. 2 Formal Rules for. 3 Using Subproofs. 4 Proof Strategies. 5 Conclusion. 1 To prove that P is false, show that a contradiction
Outline Formal roofs and Boolean Logic II Extending F with Rules for William Starr 092911 1 Review 2 Formal Rules for 3 Using Subproofs 4 roof Strategies 5 Conclusion William Starr hil 2310: Intro Logic
More informationIntroduction. I. Proof of the Minor Premise ( All reality is completely intelligible )
Philosophical Proof of God: Derived from Principles in Bernard Lonergan s Insight May 2014 Robert J. Spitzer, S.J., Ph.D. Magis Center of Reason and Faith Lonergan s proof may be stated as follows: Introduction
More informationYou submitted this quiz on Mon 14 Oct :41 PM PDT (UTC 0700). You got a score of out of
Feedback Week 2  Quiz Help You submitted this quiz on Mon 14 Oct 2013 3:41 PM PDT (UTC 0700). You got a score of 16.00 out of 16.00. Question 1 Logic of Consequence vs Logic of Appropriateness In questions
More informationHaberdashers Aske s Boys School
1 Haberdashers Aske s Boys School Occasional Papers Series in the Humanities Occasional Paper Number Sixteen Are All Humans Persons? Ashna Ahmad Haberdashers Aske s Girls School March 2018 2 Haberdashers
More informationArtificial Intelligence Prof. Deepak Khemani Department of Computer Science and Engineering Indian Institute of Technology, Madras
(Refer Slide Time: 00:14) Artificial Intelligence Prof. Deepak Khemani Department of Computer Science and Engineering Indian Institute of Technology, Madras Lecture  35 Goal Stack Planning Sussman's Anomaly
More informationChapter 3: Basic Propositional Logic. Based on Harry Gensler s book For CS2209A/B By Dr. Charles Ling;
Chapter 3: Basic Propositional Logic Based on Harry Gensler s book For CS2209A/B By Dr. Charles Ling; cling@csd.uwo.ca The Ultimate Goals Accepting premises (as true), is the conclusion (always) true?
More informationWhat is a logical argument? What is deductive reasoning? Fundamentals of Academic Writing
What is a logical argument? What is deductive reasoning? Fundamentals of Academic Writing Logical relations Deductive logic Claims to provide conclusive support for the truth of a conclusion Inductive
More informationWhat is Game Theoretical Negation?
Can BAŞKENT Institut d Histoire et de Philosophie des Sciences et des Techniques can@canbaskent.net www.canbaskent.net/logic Adam Mickiewicz University, Poznań April 1719, 2013 Outlook of the Talk Classical
More informationNegative Introspection Is Mysterious
Negative Introspection Is Mysterious Abstract. The paper provides a short argument that negative introspection cannot be algorithmic. This result with respect to a principle of belief fits to what we know
More information