sb fol iii - rensselaer polytechnic institutekryten.mm.rpi.edu/courses/intlogw/sb_fol_iii.pdf ·...
TRANSCRIPT
FOL III
Rensselaer AI & Reasoning (RAIR) LabDepartment of Cognitive Science
Department of Computer Science Lally School of Management & Technology
Rensselaer Polytechnic Institute (RPI)Troy, New York 12180 USA
Intro to Logic3/5/2018
Selmer Bringsjord
Praiseworthy AI simplicter, perhaps.
But certainly not AI = HI!
“AlphaGo, from the perspective of South, how many majuscule Roman letters are in black? Why do you say that?”
Logico-Mathematical Landscape that Has Them Turning in Their Graves
Polynomial Hierarchy
Arithmetical Hierarchy
Analytical HierarchySuper-Serious Human Cognitive Power
Serious Human Cognitive Power
Mere Calculative Cognitive Power Entscheidungsproblem
Logico-Mathematical Landscape that Has Them Turning in Their Graves
Polynomial Hierarchy
Arithmetical Hierarchy
Analytical HierarchySuper-Serious Human Cognitive Power
Serious Human Cognitive Power
Mere Calculative Cognitive Power
Descartes
Entscheidungsproblem
Logico-Mathematical Landscape that Has Them Turning in Their Graves
Polynomial Hierarchy
Arithmetical Hierarchy
Analytical HierarchySuper-Serious Human Cognitive Power
Serious Human Cognitive Power
Mere Calculative Cognitive Power
LeibnizDescartes
Entscheidungsproblem
Logico-Mathematical Landscape that Has Them Turning in Their Graves
Polynomial Hierarchy
Arithmetical Hierarchy
Analytical HierarchySuper-Serious Human Cognitive Power
Serious Human Cognitive Power
Mere Calculative Cognitive Power
Leibniz ChurchDescartes
Entscheidungsproblem
Logico-Mathematical Landscape that Has Them Turning in Their Graves
Polynomial Hierarchy
Arithmetical Hierarchy
Analytical HierarchySuper-Serious Human Cognitive Power
Serious Human Cognitive Power
Mere Calculative Cognitive Power
Leibniz ChurchDescartes Gödel
Entscheidungsproblem
Logico-Mathematical Landscape that Has Them Turning in Their Graves
Polynomial Hierarchy
Arithmetical Hierarchy
Analytical HierarchySuper-Serious Human Cognitive Power
Serious Human Cognitive Power
Mere Calculative Cognitive Power
Leibniz Church TuringDescartes Gödel
Entscheidungsproblem
Logico-Mathematical Landscape that Has Them Turning in Their Graves
Polynomial Hierarchy
Arithmetical Hierarchy
Analytical HierarchySuper-Serious Human Cognitive Power
Serious Human Cognitive Power
Mere Calculative Cognitive Power
Leibniz Church TuringDescartes Gödel
Entscheidungsproblem
Logico-Mathematical Landscape that Has Them Turning in Their Graves
Polynomial Hierarchy
Arithmetical Hierarchy
Analytical HierarchySuper-Serious Human Cognitive Power
Serious Human Cognitive Power
Mere Calculative Cognitive Power
Leibniz Church TuringDescartes Gödel
Entscheidungsproblem
Logico-Mathematical Landscape that Has Them Turning in Their Graves
Polynomial Hierarchy
Arithmetical Hierarchy
Analytical HierarchySuper-Serious Human Cognitive Power
Serious Human Cognitive Power
Mere Calculative Cognitive Power
Leibniz Church TuringDescartes Gödel
Entscheidungsproblem
Logico-Mathematical Landscape that Has Them Turning in Their Graves
Polynomial Hierarchy
Arithmetical Hierarchy
Analytical HierarchySuper-Serious Human Cognitive Power
Serious Human Cognitive Power
Mere Calculative Cognitive Power
Leibniz Church TuringDescartes Gödel
Entscheidungsproblem
Logico-Mathematical Landscape that Has Them Turning in Their Graves
Polynomial Hierarchy
Arithmetical Hierarchy
Analytical HierarchySuper-Serious Human Cognitive Power
Serious Human Cognitive Power
Mere Calculative Cognitive Power
Leibniz Church TuringDescartes Gödel
Entscheidungsproblem
Logico-Mathematical Landscape that Has Them Turning in Their Graves
Polynomial Hierarchy
Arithmetical Hierarchy
Analytical Hierarchy
Serious Human Cognitive Power
Mere Calculative Cognitive Power
Leibniz Church TuringDescartes Gödel
Entscheidungsproblem
Logico-Mathematical Landscape that Has Them Turning in Their Graves
Polynomial Hierarchy
Arithmetical Hierarchy
Analytical Hierarchy
Mere Calculative Cognitive Power
Leibniz Church TuringDescartes Gödel
Entscheidungsproblem
Logico-Mathematical Landscape that Has Them Turning in Their Graves
Polynomial Hierarchy
Arithmetical Hierarchy
Analytical Hierarchy
Leibniz Church TuringDescartes Gödel
Entscheidungsproblem
Logico-Mathematical Landscape that Has Them Turning in Their Graves
Polynomial Hierarchy
Arithmetical Hierarchy
Analytical Hierarchy
Leibniz Church Turing
P ✓ NP ✓ PSPACE = NPSPACE ✓ EXPTIME ✓ NEXPTIME ✓ EXPSPACE
Descartes Gödel
Entscheidungsproblem
Logico-Mathematical Landscape that Has Them Turning in Their Graves
Polynomial Hierarchy
Arithmetical Hierarchy
Analytical Hierarchy
Leibniz Church Turing
P ✓ NP ✓ PSPACE = NPSPACE ✓ EXPTIME ✓ NEXPTIME ✓ EXPSPACE
⌃0
⌃1
⇧1
⌃2
⇧2
...Descartes Gödel
Entscheidungsproblem
Logico-Mathematical Landscape that Has Them Turning in Their Graves
Polynomial Hierarchy
Arithmetical Hierarchy
Analytical Hierarchy
Leibniz Church Turing
Go: AlphaGo
P ✓ NP ✓ PSPACE = NPSPACE ✓ EXPTIME ✓ NEXPTIME ✓ EXPSPACE
⌃0
⌃1
⇧1
⌃2
⇧2
...Descartes Gödel
Entscheidungsproblem
Logico-Mathematical Landscape that Has Them Turning in Their Graves
Polynomial Hierarchy
Arithmetical Hierarchy
Analytical Hierarchy
Leibniz Church Turing
Go: AlphaGoJeopardy!: Watson
P ✓ NP ✓ PSPACE = NPSPACE ✓ EXPTIME ✓ NEXPTIME ✓ EXPSPACE
⌃0
⌃1
⇧1
⌃2
⇧2
...Descartes Gödel
Entscheidungsproblem
Logico-Mathematical Landscape that Has Them Turning in Their Graves
Polynomial Hierarchy
Arithmetical Hierarchy
Analytical Hierarchy
Leibniz Church Turing
Go: AlphaGoJeopardy!: WatsonChess: Deep Blue
P ✓ NP ✓ PSPACE = NPSPACE ✓ EXPTIME ✓ NEXPTIME ✓ EXPSPACE
⌃0
⌃1
⇧1
⌃2
⇧2
...Descartes Gödel
Entscheidungsproblem
Logico-Mathematical Landscape that Has Them Turning in Their Graves
Polynomial Hierarchy
Arithmetical Hierarchy
Analytical Hierarchy
Leibniz Church Turing
Checkers: ChinookGo: AlphaGoJeopardy!: Watson
Chess: Deep Blue
P ✓ NP ✓ PSPACE = NPSPACE ✓ EXPTIME ✓ NEXPTIME ✓ EXPSPACE
⌃0
⌃1
⇧1
⌃2
⇧2
...Descartes Gödel
Entscheidungsproblem
Logico-Mathematical Landscape that Has Them Turning in Their Graves
Polynomial Hierarchy
Arithmetical Hierarchy
Analytical Hierarchy
Checkers: ChinookGo: AlphaGoJeopardy!: Watson
Chess: Deep Blue
P ✓ NP ✓ PSPACE = NPSPACE ✓ EXPTIME ✓ NEXPTIME ✓ EXPSPACE
⌃0
⌃1
⇧1
⌃2
⇧2
...Leibniz Church TuringDescartes Gödel
Entscheidungsproblem
Logico-Mathematical Landscape that Has Them Turning in Their Graves
Polynomial Hierarchy
Arithmetical Hierarchy
Analytical Hierarchy
Checkers: ChinookGo: AlphaGoJeopardy!: Watson
Chess: Deep Blue
P ✓ NP ✓ PSPACE = NPSPACE ✓ EXPTIME ✓ NEXPTIME ✓ EXPSPACE
⌃0
⌃1
⇧1
⌃2
⇧2
...Leibniz Church TuringDescartes
Entscheidungsproblem
Logico-Mathematical Landscape that Has Them Turning in Their Graves
Polynomial Hierarchy
Arithmetical Hierarchy
Analytical Hierarchy
Checkers: ChinookGo: AlphaGoJeopardy!: Watson
Chess: Deep Blue
P ✓ NP ✓ PSPACE = NPSPACE ✓ EXPTIME ✓ NEXPTIME ✓ EXPSPACE
⌃0
⌃1
⇧1
⌃2
⇧2
...Leibniz TuringDescartes
Entscheidungsproblem
Logico-Mathematical Landscape that Has Them Turning in Their Graves
Polynomial Hierarchy
Arithmetical Hierarchy
Analytical Hierarchy
Checkers: ChinookGo: AlphaGoJeopardy!: Watson
Chess: Deep Blue
P ✓ NP ✓ PSPACE = NPSPACE ✓ EXPTIME ✓ NEXPTIME ✓ EXPSPACE
⌃0
⌃1
⇧1
⌃2
⇧2
...Leibniz Turing
Entscheidungsproblem
Logico-Mathematical Landscape that Has Them Turning in Their Graves
Polynomial Hierarchy
Arithmetical Hierarchy
Analytical Hierarchy
Checkers: ChinookGo: AlphaGoJeopardy!: Watson
Chess: Deep Blue
P ✓ NP ✓ PSPACE = NPSPACE ✓ EXPTIME ✓ NEXPTIME ✓ EXPSPACE
⌃0
⌃1
⇧1
⌃2
⇧2
...Leibniz
Entscheidungsproblem
Logico-Mathematical Landscape that Has Them Turning in Their Graves
Polynomial Hierarchy
Arithmetical Hierarchy
Analytical Hierarchy
Checkers: ChinookGo: AlphaGoJeopardy!: Watson
Chess: Deep Blue
P ✓ NP ✓ PSPACE = NPSPACE ✓ EXPTIME ✓ NEXPTIME ✓ EXPSPACE
⌃0
⌃1
⇧1
⌃2
⇧2
...
Entscheidungsproblem
Rengo Kriegspiel
“One of the authors has personally played this game, and it’s intriguing to think that it’s possible he has played the hardest game in the world, which cannot even in principle be played by any algorithm. (Hearn & Domaine 2009, sect 3.4.2, para. 2)
Tabular “Deduction”: It’s Taught!
18
XIMHO very bad idea—if before real learning of deduction to answer “Why, exactly? Prove it!”
Our Final New Inference Rule in FOL
• existential elimination (intuitively put):
• If we know that (i) there’s something x which is an R, and (ii) on the supposition that a is an arbitrary representative (a “witness”) of such an x we can prove P, then we are permitted to deduce P from (i) alone.
Starting State of Workspace
“Each and every thing is either a player or a referee.”
(Assumes a domain of e.g. players on a March-madness basketball court.)
Starting State of Workspace
“Each and every thing is either a player or a referee.”
“All players are tall.”
(Assumes a domain of e.g. players on a March-madness basketball court.)
Starting State of Workspace
“Each and every thing is either a player or a referee.”
“All players are tall.”
“There’s a non-tall thing.”
(Assumes a domain of e.g. players on a March-madness basketball court.)