Existential Graphs Software Dr. Russell Herman Department of Mathematics and Statistics University of North Carolina at Wilmington August 2003.

Slides:



Advertisements
Similar presentations
Artificial Intelligence
Advertisements

Logic Gates.
1 Section 1.5 Rules of Inference. 2 Definitions Theorem: a statement that can be shown to be true Proof: demonstration of truth of theorem –consists of.
The Foundations: Logic and Proofs
TRACK 2™ Version 5 The ultimate process management software.
Chapter 1 The Logic of Compound Statements. Section 1.3 Valid & Invalid Arguments.
CS128 – Discrete Mathematics for Computer Science
Discrete Mathematics Lecture 2 Alexander Bukharovich New York University.
Let remember from the previous lesson what is Knowledge representation
33 CHAPTER Basic APPLICATION SOFTWARE. © 2005 The McGraw-Hill Companies, Inc. All Rights Reserved. 1-2 Lecture Objectives More Spreadsheet Features What.
Logical and Rule-Based Reasoning Part I. Logical Models and Reasoning Big Question: Do people think logically?
Propositional Calculus Math Foundations of Computer Science.
Digital Fundamentals with PLD Programming Floyd Chapter 4
Predicates and Quantifiers
Formal Theories SIE 550 Lecture Matt Dube Doctoral Student - Spatial.
CSCI 115 Chapter 2 Logic. CSCI 115 §2.1 Propositions and Logical Operations.
Advanced Excel for Finance Professionals A self study material from South Asian Management Technologies Foundation.
Copyright © Curt Hill Truth Tables A way to show Boolean Operations.
Artificial intelligence project
Chapter 2 The Logic of Quantified Statements. Section 2.4 Arguments with Quantified Statements.
1 Sections 1.5 & 3.1 Methods of Proof / Proof Strategy.
Chapter 1, Part II: Predicate Logic With Question/Answer Animations.
COS 150 Discrete Structures Assoc. Prof. Svetla Boytcheva Fall semester 2014.
Arguments with Quantified Statements M Universal Instantiation If some property is true for everything in a domain, then it is true of any particular.
First Order Logic Lecture 2: Sep 9. This Lecture Last time we talked about propositional logic, a logic on simple statements. This time we will talk about.
Chapter 1, Part II: Predicate Logic With Question/Answer Animations.
Microsoft ® Office Excel 2003 Training Using XML in Excel SynAppSys Educational Services presents:
Propositional Calculus CS 270: Mathematical Foundations of Computer Science Jeremy Johnson.
Chapter 3: Introduction to Logic. Logic Main goal: use logic to analyze arguments (claims) to see if they are valid or invalid. This is useful for math.
Chapter 2 The Logic of Quantified Statements. Section 2.1 Intro to Predicates & Quantified Statements.
Thinking Mathematically
Propositional Logic Predicate Logic
PERFORMING CALCULATIONS Microsoft Excel. Excel Formulas A formula is a set of mathematical instructions that can be used in Excel to perform calculations.
Floyd, Digital Fundamentals, 10 th ed Digital Fundamentals Tenth Edition Floyd Chapter 4 © 2008 Pearson Education.
Chapter 7. Propositional and Predicate Logic Fall 2013 Comp3710 Artificial Intelligence Computing Science Thompson Rivers University.
Dilemma: Division Into Cases Dilemma: p  q p  r q  r  r Premises:x is positive or x is negative. If x is positive, then x 2 is positive. If x is negative,
Introduction to Digital Electronics Lecture 5: Function Minimisation.
The Existential Graphs Project Rensselaer Reasoning Group September 12, 2001.
Foundations of Discrete Mathematics Chapter 1 By Dr. Dalia M. Gil, Ph.D.
Lecture 11 Introduction to R and Accessing USGS Data from Web Services Jeffery S. Horsburgh Hydroinformatics Fall 2013 This work was funded by National.
Deductive Reasoning. Inductive: premise offers support and evidenceInductive: premise offers support and evidence Deductive: premises offers proof that.
To play, start slide show and click on circle Access 1 Access 2 Access 3 Access 4 Access Access
Truth Table to Statement Form
Chapter 7. Propositional and Predicate Logic
3. The Logic of Quantified Statements Summary
DeMorgan’s Theorem DeMorgan’s 2nd Theorem
Logic Gates.
Logic Gates Benchmark Companies Inc PO Box Aurora CO
Data Validation and Protecting Workbook
Introduction to Prolog
Chapter 2.3 Binary Logic.
Propositional Calculus: Boolean Functions and Expressions
Applications of Propositional Logic
Logical Inferences: A set of premises accompanied by a suggested conclusion regardless of whether or not the conclusion is a logical consequence of the.
DESICION TABLE Decision tables are precise and compact way to model complicated logic. Decision table is useful when input and output data can be.
Logic Gates.
TRUTH TABLES.
TRUTH TABLES continued.
Computer Security: Art and Science, 2nd Edition
Digital Fundamentals Floyd Chapter 4 Tenth Edition
Deductive Arguments: More Truth Tables
Spreadsheets, Modelling & Databases
Lecture 5 Binary Operation Boolean Logic. Binary Operations Addition Subtraction Multiplication Division.
Section 3.7 Switching Circuits
XOR Function Logic Symbol  Description  Truth Table 
Predicates and Quantifiers
Logical and Rule-Based Reasoning Part I
The Foundations: Logic and Proofs
Rules of inference Section 1.5 Monday, December 02, 2019
Presentation transcript:

Existential Graphs Software Dr. Russell Herman Department of Mathematics and Statistics University of North Carolina at Wilmington August 2003

Overview Test engine Using Peirce’s Alpha Model for Existential Graphs. Designed to test the engine Not ready for the end user. Ultimate Goal: To make assertions using predicate logic. Outline of Talk Introduce the Interface Simple Examples Future Development All men are mortal. Socrates is a man. Therefore ?????

Interface – Engine Test Expression Entry Variable List Truth Table – Full or Select Parsed Expressions Conclusions- not implemented yet

Interface – Menu Items Built-in Examples Modus Ponens Modus Tollens Conditional Instructions Symbols

Example 1 - Not A and B The Steps for Entering this Expression Type in Expression Not = ~ And = + A, B can also be full words or phrases But cannot be one of ~, +, *, (, ) Example later Click on Add The expression is parsed

Example 1 – Not A and B Add Expression Variables Expression Sheet of Assertion Truth Table 0’s - True 1’s - False Assert Determine when the expressions are true together A - False B - True

Example 2: Modus Ponens Add Several Expressions Conditional > A>B means “If A then B” Truth Table => Click Assert Only True when both A and B are True

Example 3 – Apples and Oranges Can Use Words Add Statements: Apples and Oranges and If Apples, then Bananas Truth Table Conjunction of last 2 columns true? Assert & Conclude Apples, Oranges and Bananas are all true

Pocket PC Version - Expressions Modus Ponens and Modus Tollens

Pocket PC Version - Tables Assertion Table only shows rows in which all assertions are true. Here is Modus Ponens from which only B true (0) can be concluded.

Pocket PC Version – 4 Variables Apples and Oranges Several Variables with many characters The Assertion Table only lists rows in which conjunction of expressions is true.

What is Missing to Date? 1. Automated – Minimum User Input 2. Read Large Sets of Statements 3. Output Conclusions 4. Use Quantifiers – All, Some, None, … Requires Peirce’s Beta Model

What is Doable? 1. Automated and Read Text Files Hide Engine Allow Manual Entry or Read Text Parse words like “and”, “or”, “not”, “if.. then” Last Two Features have recently been added!

Read Text Files Create the Text File Open File Parse Assert Results: Red - False (1) Blue - False (1) Green - True (0) Yellow - False (1)

Expressions with “and”, “or”, “not” Create Text File But without symbols Open File, Parse and Assert The Conclusions are the same as before

Last Example Results: A - ? (0 or 1) B - False (1) C - True (0) Enter and Add Two Expressions Assert What can one conclude?

What needs work 1. Automate Conclusions May output simple combinations of statements May need user input to determine what types of combinations 2. Implement Peirce’s Beta/Gamma Logic Alpha version is equivalent to Boolean Logic Beta Version follows basic rules and free of user creativity

Summary We have a prototypical engine that can Create truth tables Parse simple statements Can read in sets of statements from files Check validity of non-quantified statement sets We seek an engine that Is more automated Can treat quantifiers (all, some, none) Can parse more complicated statements Can make logical conclusions automatically

Thank you! A copy of this presentation is located at Questions and suggestions can be directed to Dr. Russell Herman Or Dr. Pattricia Turrisi UNC Wilmington, Wilmington, NC