The Validity and Soundness of Arguments - Kansas State University
[Pages:30]Outline Introduction Atomic Sentences (summary) Logical Consequence Demonstrating Non-consequence
The Validity and Soundness of Arguments
Torben Amtoft Kansas State University
Torben Amtoft Kansas State University
The Validity and Soundness of Arguments
Outline Introduction Atomic Sentences (summary) Logical Consequence Demonstrating Non-consequence
Introduction
Atomic Sentences (summary)
Logical Consequence
Demonstrating Non-consequence
Torben Amtoft Kansas State University
The Validity and Soundness of Arguments
Outline Introduction Atomic Sentences (summary) Logical Consequence Demonstrating Non-consequence
Road Map
Two main aims of book (p.2): 1. help you learn language of first-order logic (FOL) 2. help you learn notion of logical consequence
Torben Amtoft Kansas State University
The Validity and Soundness of Arguments
Outline Introduction Atomic Sentences (summary) Logical Consequence Demonstrating Non-consequence
Road Map
Two main aims of book (p.2): 1. help you learn language of first-order logic (FOL) 2. help you learn notion of logical consequence Chapter 1 takes the first step of (1) Chapter 2 takes the first step of (2)
Torben Amtoft Kansas State University
The Validity and Soundness of Arguments
Outline Introduction Atomic Sentences (summary) Logical Consequence Demonstrating Non-consequence
Atomic Sentences
A term t is built from constants and function symbols: father(father(max))
An atomic sentence is a predicate applied to some terms: Older(father(max),max)
Torben Amtoft Kansas State University
The Validity and Soundness of Arguments
Outline Introduction Atomic Sentences (summary) Logical Consequence Demonstrating Non-consequence
Atomic Sentences
A term t is built from constants and function symbols: father(father(max))
An atomic sentence is a predicate applied to some terms: Older(father(max),max)
result is spelling is can be nested?
functions object lower case yes
predicates truth value capitalized no
Torben Amtoft Kansas State University
The Validity and Soundness of Arguments
Outline Introduction Atomic Sentences (summary) Logical Consequence Demonstrating Non-consequence
Example Worlds
Arithmetic Family Tarski's World
constants
0,1,2,. . . max, claire a, b, . . .
functions arity 1 arity 2 sin, cos +,father
predicates arity 1 arity 2
< Pet Older Cube LeftOf
many functions and predicates with arity 2 are written infix: x + y, x < y, x = y
functions can be added to Tarski's world (p.33, and homework exercises 1.13 & 1.14)
The identity predicate "=" is relevant in all worlds!
Torben Amtoft Kansas State University
The Validity and Soundness of Arguments
Outline Introduction Atomic Sentences (summary) Logical Consequence Demonstrating Non-consequence
Motivation
An argument is not two persons arguing back and forth, but
one person presenting a series of statements in which one, the conclusion, is meant to be a consequence of the others, called the premises.
Torben Amtoft Kansas State University
The Validity and Soundness of Arguments
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