A Judgmental Formulation of Modal Logic


 Diane Carter
 4 years ago
 Views:
Transcription
1 A Judgmental Formulation of Modal Logic Sungwoo Park Pohang University of Science and Technology South Korea Estonian Theory Days Jan 30, 2009
2 Outline Study of logic Model theory vs Proof theory Classical logic vs Constructive logic Judgmental analysis of propositional logic Modal logic Summary 2
3 Model vs. Proof Model I Model theory Eg. assignment of truth values Semantic consequence A 1,, A n I C A 1,, A n C Proof theory Inference rules use premises to obtain the conclusion Syntactic entailment A 1,, A n C 3
4 Classical Logic Every proposition is either true or false. Concerned with: "whether a given proposition is true or not." Tautologies in classical logic 4
5 Constructive Logic We know only what we can prove. Concerned with: "how a given proposition becomes true." Not provable in constructive logic 5
6 This talk is about Constructive Proof Theory. Per MartinLöf. On the meaning of the logical constants and the justifications of the logical laws, Nordic Journal of Philosophical Logic, 1(1):1160, Frank Pfenning and Rowan Davies. A judgmental reconstruction of modal logic, Mathematical Structures in Computer Science, 11(4) , 2001.
7 Outline Study of logic Model theory vs Proof theory Classical logic vs Constructive logic Judgmental analysis of propositional logic Judgmental analysis of modal logic Summary 7
8 Judgments and Proofs A judgment = an object of knowledge that may or may not be provable. If there exists a proof, the judgment becomes evident. we know the judgment. Examples "11 is equal to 0" is true. "1 + 1 is equal to 0" is false. "It is snowing" is true. "11 is equal to 0" is false. 8
9 Inference Rules and Axioms A proof consists of applications of inference rules. J i are premises (1 i n). J is a conclusion. "If J 1 through J n (premises) hold, then J (conclusion) holds." If n = 0 (no premise), the inference rule is an axiom. 9
10 Proposition A statement such that we know what counts as a verification of it. If A is a proposition, we know how to check the validity of the proof of its truth. Example: "It is raining." Secondary notion 10
11 Proposition Without arithmetic rules, what is the meaning of "11 is equal to 0"? 11
12 Propositions Propositional Logic Judgments: 12
13 Natural Deduction System Introduced by Gentzen, 1934 For each connective,,,... introduction rule: how to establish a proof elimination rule: how to exploit an existing proof 13
14 Implication 14
15 Disjunction 15
16 Truth and Falsehood 16
17 What if Elimination Rules were Too strong Too weak 17
18 Elimination Rules are OK Local soundness Elimination rules are not too strong. Local completeness Elimination rules are not too weak 18
19 Local Soundness and Completeness 19
20 Definition Hypothetical Judgments Substitution principle 20
21 Inference Rules 21
22 Study of logic Outline Judgmental analysis of propositional logic Judgmental analysis of modal logic Modal necessity Modal possibility Lax modality O Summary 22
23 POSTECH 23
24 Modalities and A : necessarily A A : possibly A Spatial interpretation: A : everywhere A A : somewhere A Temporal interpretation: A : always A A : sometime A Modal Logic 24
25 Modal necessity First Judgments, Then Propositions.
26 Validity Judgment A valid A is valid if A is true at a world about which we know nothing, or at any world. Modal proposition A Introduction rule 26
27 New Forms of Hypothetical Judgments Definition Substitution principle 27
28 Modal necessity 28
29 Local Soundness and Completeness 29
30 Axiomatic Characterization (S4) 30
31 Modal possibility Again, First Judgments, Then Propositions.
32 Possibility Judgment A poss A is possibly true if A is true at a certain world. 32
33 Modal possibility 33
34 Local Soundness and Completeness 34
35 Axiomatic Characterization 35
36 Lax modality O Yet again, First Judgments, Then Propositions.
37 Lax Judgment A lax A is true under a certain constraint. 37
38 Lax Modality O 38
39 Local Soundness and Completeness 39
40 Axiomatic Characterization 40
41 Study of logic Outline Judgmental analysis of propositional logic Judgmental analysis of modal logic Modal necessity Modal possibility Lax modality O Summary 41
42 Applications, Type system for staged computation Type system for distributed computation O Type system for effectful computation Monad in functional language Haskell 42
43 Internalizing Normal Proofs Normal proofs Internalizing normal proofs using a modality Introduction and elimination rules 43
44 Uses two judgments Sequent Calculus Satisfies cutelimination 44
45 Thank you.
Artificial 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 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 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 informationLogic and Pragmatics: linear logic for inferential practice
Logic and Pragmatics: linear logic for inferential practice Daniele Porello danieleporello@gmail.com Institute for Logic, Language & Computation (ILLC) University of Amsterdam, Plantage Muidergracht 24
More informationLecture Notes on Classical Logic
Lecture Notes on Classical Logic 15317: Constructive Logic William Lovas Lecture 7 September 15, 2009 1 Introduction In this lecture, we design a judgmental formulation of classical logic To gain an intuition,
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 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 informationBoghossian & Harman on the analytic theory of the a priori
Boghossian & Harman on the analytic theory of the a priori PHIL 83104 November 2, 2011 Both Boghossian and Harman address themselves to the question of whether our a priori knowledge can be explained in
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 informationEntailment, with nods to Lewy and Smiley
Entailment, with nods to Lewy and Smiley Peter Smith November 20, 2009 Last week, we talked a bit about the AndersonBelnap logic of entailment, as discussed in Priest s Introduction to NonClassical Logic.
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 informationReductio ad Absurdum, Modulation, and Logical Forms. Miguel LópezAstorga 1
International Journal of Philosophy and Theology June 25, Vol. 3, No., pp. 5965 ISSN: 2333575 (Print), 23335769 (Online) Copyright The Author(s). All Rights Reserved. Published by American Research
More informationEvaluating Classical Identity and Its Alternatives by Tamoghna Sarkar
Evaluating Classical Identity and Its Alternatives by Tamoghna Sarkar Western Classical theory of identity encompasses either the concept of identity as introduced in the firstorder logic or language
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 informationWhat is the Nature of Logic? Judy Pelham Philosophy, York University, Canada July 16, 2013 PanHellenic Logic Symposium Athens, Greece
What is the Nature of Logic? Judy Pelham Philosophy, York University, Canada July 16, 2013 PanHellenic Logic Symposium Athens, Greece Outline of this Talk 1. What is the nature of logic? Some history
More informationReview of "The Tarskian Turn: Deflationism and Axiomatic Truth"
Essays in Philosophy Volume 13 Issue 2 Aesthetics and the Senses Article 19 August 2012 Review of "The Tarskian Turn: Deflationism and Axiomatic Truth" Matthew McKeon Michigan State University Follow this
More informationPhilosophy of Mathematics Kant
Philosophy of Mathematics Kant Owen Griffiths oeg21@cam.ac.uk St John s College, Cambridge 20/10/15 Immanuel Kant Born in 1724 in Königsberg, Prussia. Enrolled at the University of Königsberg in 1740 and
More informationG. H. von Wright Deontic Logic
G. H. von Wright Deontic Logic Kian MintzWoo University of Amsterdam January 9, 2009 January 9, 2009 Logic of Norms 2010 1/17 INTRODUCTION In von Wright s 1951 formulation, deontic logic is intended to
More informationBeyond Symbolic Logic
Beyond Symbolic Logic 1. The Problem of Incompleteness: Many believe that mathematics can explain *everything*. Gottlob Frege proposed that ALL truths can be captured in terms of mathematical entities;
More informationprohibition, moral commitment and other normative matters. Although often described as a branch
Logic, deontic. The study of principles of reasoning pertaining to obligation, permission, prohibition, moral commitment and other normative matters. Although often described as a branch of logic, deontic
More informationInstrumental reasoning* John Broome
Instrumental reasoning* John Broome For: Rationality, Rules and Structure, edited by Julian NidaRümelin and Wolfgang Spohn, Kluwer. * This paper was written while I was a visiting fellow at the Swedish
More informationInternational Phenomenological Society
International Phenomenological Society The Semantic Conception of Truth: and the Foundations of Semantics Author(s): Alfred Tarski Source: Philosophy and Phenomenological Research, Vol. 4, No. 3 (Mar.,
More informationLogical Constants as Punctuation Marks
362 Notre Dame Journal of Formal Logic Volume 30, Number 3, Summer 1989 Logical Constants as Punctuation Marks KOSTA DOSEN* Abstract This paper presents a prooftheoretical approach to the question "What
More informationA Liar Paradox. Richard G. Heck, Jr. Brown University
A Liar Paradox Richard G. Heck, Jr. Brown University It is widely supposed nowadays that, whatever the right theory of truth may be, it needs to satisfy a principle sometimes known as transparency : Any
More informationPredicate logic. Miguel Palomino Dpto. Sistemas Informáticos y Computación (UCM) Madrid Spain
Predicate logic Miguel Palomino Dpto. Sistemas Informáticos y Computación (UCM) 28040 Madrid Spain Synonyms. Firstorder logic. Question 1. Describe this discipline/subdiscipline, and some of its more
More informationLogic I or Moving in on the Monkey & Bananas Problem
Logic I or Moving in on the Monkey & Bananas Problem We said that an agent receives percepts from its environment, and performs actions on that environment; and that the action sequence can be based on
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 informationIs the law of excluded middle a law of logic?
Is the law of excluded middle a law of logic? Introduction I will conclude that the intuitionist s attempt to rule out the law of excluded middle as a law of logic fails. They do so by appealing to harmony
More informationDoes Deduction really rest on a more secure epistemological footing than Induction?
Does Deduction really rest on a more secure epistemological footing than Induction? We argue that, if deduction is taken to at least include classical logic (CL, henceforth), justifying CL  and thus deduction
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 informationA Generalization of Hume s Thesis
Philosophia Scientiæ Travaux d'histoire et de philosophie des sciences 101 2006 Jerzy Kalinowski : logique et normativité A Generalization of Hume s Thesis Jan Woleński Publisher Editions Kimé Electronic
More informationBOOK REVIEWS. About a new solution to the problem of future contingents
Logic and Logical Philosophy Volume 26 (2017), 277 281 DOI: 10.12775/LLP.2016.024 BOOK REVIEWS About a new solution to the problem of future contingents Marcin Tkaczyk, Futura contingentia, Wydawnictwo
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 informationProof as a cluster concept in mathematical practice. Keith Weber Rutgers University
Proof as a cluster concept in mathematical practice Keith Weber Rutgers University Approaches for defining proof In the philosophy of mathematics, there are two approaches to defining proof: Logical or
More informationHow Gödelian Ontological Arguments Fail
How Gödelian Ontological Arguments Fail Matthew W. Parker Abstract. Ontological arguments like those of Gödel (1995) and Pruss (2009; 2012) rely on premises that initially seem plausible, but on closer
More informationGROUNDING AND LOGICAL BASING PERMISSIONS
Diametros 50 (2016): 81 96 doi: 10.13153/diam.50.2016.979 GROUNDING AND LOGICAL BASING PERMISSIONS Diego Tajer Abstract. The relation between logic and rationality has recently reemerged as an important
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 information2.4 Notational Definition
24 Notational Definition 15 24 Notational Definition The jdgments, propositions, and inference rles we have defined so far collectively form a system of natral dedction It is a minor variant of a system
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 informationSemantics and the Justification of Deductive Inference
Semantics and the Justification of Deductive Inference Ebba Gullberg ebba.gullberg@philos.umu.se Sten Lindström sten.lindstrom@philos.umu.se Umeå University Abstract Is it possible to give a justification
More informationCircumscribing Inconsistency
Circumscribing Inconsistency Philippe Besnard IRISA Campus de Beaulieu F35042 Rennes Cedex Torsten H. Schaub* Institut fur Informatik Universitat Potsdam, Postfach 60 15 53 D14415 Potsdam Abstract We
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 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 informationBroad on Theological Arguments. I. The Ontological Argument
Broad on God Broad on Theological Arguments I. The Ontological Argument Sample Ontological Argument: Suppose that God is the most perfect or most excellent being. Consider two things: (1)An entity that
More informationAppeared in: AlMukhatabat. A Trilingual Journal For Logic, Epistemology and Analytical Philosophy, Issue 6: April 2013.
Appeared in: AlMukhatabat. A Trilingual Journal For Logic, Epistemology and Analytical Philosophy, Issue 6: April 2013. Panu Raatikainen Intuitionistic Logic and Its Philosophy Formally, intuitionistic
More informationConditionals II: no truth conditions?
Conditionals II: no truth conditions? UC Berkeley, Philosophy 142, Spring 2016 John MacFarlane 1 Arguments for the material conditional analysis As Edgington [1] notes, there are some powerful reasons
More informationIntuitive evidence and formal evidence in proofformation
Intuitive evidence and formal evidence in proofformation Okada Mitsuhiro Section I. Introduction. I would like to discuss proof formation 1 as a general methodology of sciences and philosophy, with a
More informationConstructive Logic, Truth and Warranted Assertibility
Constructive Logic, Truth and Warranted Assertibility Greg Restall Department of Philosophy Macquarie University Version of May 20, 2000....................................................................
More informationLOGIC LECTURE #3: DEDUCTION AND INDUCTION. Source: A Concise Introduction to Logic, 11 th Ed. (Patrick Hurley, 2012)
LOGIC LECTURE #3: DEDUCTION AND INDUCTION Source: A Concise Introduction to Logic, 11 th Ed. (Patrick Hurley, 2012) Deductive Vs. Inductive If the conclusion is claimed to follow with strict certainty
More informationInstructor s Manual 1
Instructor s Manual 1 PREFACE This instructor s manual will help instructors prepare to teach logic using the 14th edition of Irving M. Copi, Carl Cohen, and Kenneth McMahon s Introduction to Logic. The
More informationLonergan on General Transcendent Knowledge. In General Transcendent Knowledge, Chapter 19 of Insight, Lonergan does several things:
Lonergan on General Transcendent Knowledge In General Transcendent Knowledge, Chapter 19 of Insight, Lonergan does several things: 13He provides a radical reinterpretation of the meaning of transcendence
More informationIS THE SYLLOGISTIC A LOGIC? it is not a theory or formal ontology, a system concerned with general features of the
IS THE SYLLOGISTIC A LOGIC? Much of the last fifty years of scholarship on Aristotle s syllogistic suggests a conceptual framework under which the syllogistic is a logic, a system of inferential reasoning,
More informationAn alternative understanding of interpretations: Incompatibility Semantics
An alternative understanding of interpretations: Incompatibility Semantics 1. In traditional (truththeoretic) semantics, interpretations serve to specify when statements are true and when they are false.
More informationBob Hale: Necessary Beings
Bob Hale: Necessary Beings Nils Kürbis In Necessary Beings, Bob Hale brings together his views on the source and explanation of necessity. It is a very thorough book and Hale covers a lot of ground. It
More informationOn Priest on nonmonotonic and inductive logic
On Priest on nonmonotonic and inductive logic Greg Restall School of Historical and Philosophical Studies The University of Melbourne Parkville, 3010, Australia restall@unimelb.edu.au http://consequently.org/
More informationAll They Know: A Study in MultiAgent Autoepistemic Reasoning
All They Know: A Study in MultiAgent Autoepistemic Reasoning PRELIMINARY REPORT Gerhard Lakemeyer Institute of Computer Science III University of Bonn Romerstr. 164 5300 Bonn 1, Germany gerhard@cs.unibonn.de
More informationTOWARDS A PHILOSOPHICAL UNDERSTANDING OF THE LOGICS OF FORMAL INCONSISTENCY
CDD: 160 http://dx.doi.org/10.1590/01006045.2015.v38n2.wcear TOWARDS A PHILOSOPHICAL UNDERSTANDING OF THE LOGICS OF FORMAL INCONSISTENCY WALTER CARNIELLI 1, ABÍLIO RODRIGUES 2 1 CLE and Department of
More information1.2. What is said: propositions
1.2. What is said: propositions 1.2.0. Overview In 1.1.5, we saw the close relation between two properties of a deductive inference: (i) it is a transition from premises to conclusion that is free of any
More informationHourya BENIS SINACEUR. Sciences et des Techniques (IHPST) CNRSENSUniversité Paris 1. Juin 2010
Hourya BENIS SINACEUR Institut d Histoire et Philosophie des Sciences et des Techniques (IHPST) CNRSENSUniversité Paris 1 Juin 2010 Etchemendy s objections to Tarski s account of the notion of logical
More informationCourses providing assessment data PHL 202. Semester/Year
1 Department/Program 20122016 Assessment Plan Department: Philosophy Directions: For each department/program student learning outcome, the department will provide an assessment plan, giving detailed information
More informationCan logical consequence be deflated?
Can logical consequence be deflated? Michael De University of Utrecht Department of Philosophy Utrecht, Netherlands mikejde@gmail.com in Insolubles and Consequences : essays in honour of Stephen Read,
More informationDEPARTMENT OF PHILOSOPHY FALL 2014 COURSE DESCRIPTIONS
DEPARTMENT OF PHILOSOPHY FALL 2014 COURSE DESCRIPTIONS PHIL 2300001 Beginning Philosophy 11:0011:50 MWF ENG/PHIL 264 PHIL 2300002 Beginning Philosophy 9:009:50 MWF ENG/PHIL 264 This is a general introduction
More informationReview of Philosophical Logic: An Introduction to Advanced Topics *
Teaching Philosophy 36 (4):420423 (2013). Review of Philosophical Logic: An Introduction to Advanced Topics * CHAD CARMICHAEL Indiana University Purdue University Indianapolis This book serves as a concise
More informationCan Gödel s Incompleteness Theorem be a Ground for Dialetheism? *
논리연구 202(2017) pp. 241271 Can Gödel s Incompleteness Theorem be a Ground for Dialetheism? * 1) Seungrak Choi Abstract Dialetheism is the view that there exists a true contradiction. This paper ventures
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 informationCan A Priori Justified Belief Be Extended Through Deduction? It is often assumed that if one deduces some proposition p from some premises
Can A Priori Justified Belief Be Extended Through Deduction? Introduction It is often assumed that if one deduces some proposition p from some premises which one knows a priori, in a series of individually
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 information1/9. The First Analogy
1/9 The First Analogy So far we have looked at the mathematical principles but now we are going to turn to the dynamical principles, of which there are two sorts, the Analogies of Experience and the Postulates
More informationEpistemic Logic I. An introduction to the course
Epistemic Logic I. An introduction to the course Yanjing Wang Department of Philosophy, Peking University Sept. 14th 2015 Standard epistemic logic and its dynamics Beyond knowing that: a new research program
More informationCan Negation be Defined in Terms of Incompatibility?
Can Negation be Defined in Terms of Incompatibility? Nils Kurbis 1 Introduction Every theory needs primitives. A primitive is a term that is not defined any further, but is used to define others. Thus
More informationPotentialism about set theory
Potentialism about set theory Øystein Linnebo University of Oslo SotFoM III, 21 23 September 2015 Øystein Linnebo (University of Oslo) Potentialism about set theory 21 23 September 2015 1 / 23 Openendedness
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 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 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 informationPhilosophy 125 Day 21: Overview
Branden Fitelson Philosophy 125 Lecture 1 Philosophy 125 Day 21: Overview 1st Papers/SQ s to be returned this week (stay tuned... ) Vanessa s handout on Realism about propositions to be posted Second papers/s.q.
More informationThe Context of Inference
The Context of Inference CURTIS FRANKS I am eager to examine together with you, Crito, whether this argument will appear in any way different to me in my present circumstances, or whether it remains the
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 informationKnowledge, Time, and the Problem of Logical Omniscience
Fundamenta Informaticae XX (2010) 1 18 1 IOS Press Knowledge, Time, and the Problem of Logical Omniscience RenJune Wang Computer Science CUNY Graduate Center 365 Fifth Avenue, New York, NY 10016 rwang@gc.cuny.edu
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 informationFrom Necessary Truth to Necessary Existence
Prequel for Section 4.2 of Defending the Correspondence Theory Published by PJP VII, 1 From Necessary Truth to Necessary Existence Abstract I introduce new details in an argument for necessarily existing
More informationI. In the ongoing debate on the meaning of logical connectives 1, two families of
What does & mean? Axel Arturo Barceló Aspeitia abarcelo@filosoficas.unam.mx Instituto de Investigaciones Filosóficas, UNAM México Proceedings of the TwentyFirst World Congress of Philosophy, Vol. 5, 2007.
More informationChapter 1. Introduction. 1.1 Deductive and Plausible Reasoning Strong Syllogism
Contents 1 Introduction 3 1.1 Deductive and Plausible Reasoning................... 3 1.1.1 Strong Syllogism......................... 3 1.1.2 Weak Syllogism.......................... 4 1.1.3 Transitivity
More informationFigure 1 Figure 2 U S S. nonp P P
1 Depicting negation in diagrammatic logic: legacy and prospects Fabien Schang, Amirouche Moktefi schang.fabien@voila.fr amirouche.moktefi@gersulp.ustrasbg.fr Abstract Here are considered the conditions
More informationFatalism and Truth at a Time Chad Marxen
Stance Volume 6 2013 29 Fatalism and Truth at a Time Chad Marxen Abstract: In this paper, I will examine an argument for fatalism. I will offer a formalized version of the argument and analyze one of the
More informationLOGICAL PLURALISM IS COMPATIBLE WITH MONISM ABOUT METAPHYSICAL MODALITY
LOGICAL PLURALISM IS COMPATIBLE WITH MONISM ABOUT METAPHYSICAL MODALITY Nicola Ciprotti and Luca Moretti Beall and Restall [2000], [2001] and [2006] advocate a comprehensive pluralist approach to logic,
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 informationAspects of Western Philosophy Dr. Sreekumar Nellickappilly Department of Humanities and Social Sciences Indian Institute of Technology, Madras
Aspects of Western Philosophy Dr. Sreekumar Nellickappilly Department of Humanities and Social Sciences Indian Institute of Technology, Madras Module  21 Lecture  21 Kant Forms of sensibility Categories
More informationSUPPOSITIONAL REASONING AND PERCEPTUAL JUSTIFICATION
SUPPOSITIONAL REASONING AND PERCEPTUAL JUSTIFICATION Stewart COHEN ABSTRACT: James Van Cleve raises some objections to my attempt to solve the bootstrapping problem for what I call basic justification
More informationTHESES SIS/LIBRARY TELEPHONE:
THESES SIS/LIBRARY TELEPHONE: +61 2 6125 4631 R.G. MENZIES LIBRARY BUILDING NO:2 FACSIMILE: +61 2 6125 4063 THE AUSTRALIAN NATIONAL UNIVERSITY EMAIL: library.theses@anu.edu.au CANBERRA ACT 0200 AUSTRALIA
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 informationThe Appeal to Reason. Introductory Logic pt. 1
The Appeal to Reason Introductory Logic pt. 1 Argument vs. Argumentation The difference is important as demonstrated by these famous philosophers. The Origins of Logic: (highlights) Aristotle (385322
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 10 Inference in First Order Logic I had introduced first order
More informationRichard L. W. Clarke, Notes REASONING
1 REASONING Reasoning is, broadly speaking, the cognitive process of establishing reasons to justify beliefs, conclusions, actions or feelings. It also refers, more specifically, to the act or process
More informationIs Epistemic Probability Pascalian?
Is Epistemic Probability Pascalian? James B. Freeman Hunter College of The City University of New York ABSTRACT: What does it mean to say that if the premises of an argument are true, the conclusion is
More informationTYPES, TABLEAUS, AND GODEL' S GOD
TYPES, TABLEAUS, AND GODEL' S GOD TRENDS IN LOGIC Studia Logica Library VOLUME 13 Managing Editor Ryszard Wojcicki, Institute of Philosoph y and Sociolog y. Polish Academ y of Sciences. Warsaw, Poland
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 informationAyer s linguistic theory of the a priori
Ayer s linguistic theory of the a priori phil 43904 Jeff Speaks December 4, 2007 1 The problem of a priori knowledge....................... 1 2 Necessity and the a priori............................ 2
More informationJELIA Justification Logic. Sergei Artemov. The City University of New York
JELIA 2008 Justification Logic Sergei Artemov The City University of New York Dresden, September 29, 2008 This lecture outlook 1. What is Justification Logic? 2. Why do we need Justification Logic? 3.
More informationBelief, Awareness, and TwoDimensional Logic"
Belief, Awareness, and TwoDimensional Logic" Hu Liu and Shier Ju l Institute of Logic and Cognition Zhongshan University Guangzhou, China Abstract Belief has been formally modelled using doxastic logics
More information