FOL II

Rensselaer AI & Reasoning (RAIR) LabDepartment of Cognitive ScienceDepartment of Computer Science

Lally School of Management & TechnologyRensselaer Polytechnic Institute (RPI)

Troy NY 12180 USA

Intro to Logic3/1/2018

Selmer Bringsjord

Re Test 1, HyperGrader …

Some Parameters

• # of symbols used

• time submitted (relative to publication)

• # of available givens used

• geometry (Euclidean 3-space)

Required problems now include the two Test-1 problems, converted:

http://www.logicamodernapproach.com/allProblems

Comments on Proof Plan for KingAce2

Sub-Proof 1

Sub-Proof 2

Next New (Not-So-Easy!) Inference Rule in FOL

Next New (Not-So-Easy!) Inference Rule in FOL

•universal introduction

Next New (Not-So-Easy!) Inference Rule in FOL

•universal introduction

• If something a is an R, and the constant/name a is genuinely arbitrary, then we can deduce that everything is an R.

The Inference Schema

The Inference Schema

The Inference Schema

(Why the provisos?)

Example

Example

X

Example

X

X

Example

X

X

Let’s explore in Slate, by first constructing this example from scratch …

Practice Problems in Slate!

Practice Problems in Slate!

{8x(R(x) $ S(x)), 8xR(x)} ` 8xS(x)} ?

Practice Problems in Slate!

{8x(R(x) $ S(x)), 8xR(x)} ` 8xS(x)} ?

{8x[Norsk(x) ! 8y(Svensk(y) ! Smarter(x, y))]} ` 8x, y[(Norsk(x) ^ Svensk(y)) ! Smarter(x, y)] ?

Practice Problems in Slate!

{8x(R(x) $ S(x)), 8xR(x)} ` 8xS(x)} ?

{8x[Norsk(x) ! 8y(Svensk(y) ! Smarter(x, y))]} ` 8x, y[(Norsk(x) ^ Svensk(y)) ! Smarter(x, y)] ?

{8x, y[(Norsk(x) ^ (Svensk(y)) ! Smarter(x, y)],

8x, y[(Svensk(x) ^ (Dansk(y)) ! Smarter(x, y)]} `

8x, y[(Norsk(x) ^ (Dansk(y)) ! Smarter(x, y)] ?