Meditation for a Theorem Prover Reasoning and Consciousness - - PowerPoint PPT Presentation

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Meditation for a Theorem Prover Reasoning and Consciousness - - PowerPoint PPT Presentation

Dec 19, 2023 160 likes •716 views

Meditation for a Theorem Prover Reasoning and Consciousness Teaching a Theorem Prover to let its Mind Wander Ulrich Furbach Claudia Schon Univ. Koblenz - DFG Project Cognitive Reasoning Reasoning and Consciousness Teaching a

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Meditation for a Theorem Prover

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Reasoning and Consciousness
 Teaching a Theorem Prover to let its Mind Wander

Ulrich Furbach Claudia Schon

  • Univ. Koblenz - DFG Project ‚Cognitive Reasoning‘
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Reasoning and Consciousness
 Teaching a Theorem Prover to let its Mind Wander

Ulrich Furbach Claudia Schon

  • Univ. Koblenz - DFG Project ‚Cognitive Reasoning‘
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Reasoning and Consciousness
 Teaching a Theorem Prover to let its Mind Wander

Ulrich Furbach Claudia Schon

  • Univ. Koblenz - DFG Project ‚Cognitive Reasoning‘
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My body cast a shadow over the grass. What was the CAUSE of this? a) The sun was rising. b) The grass was cut. COPA Benchmarks

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My body cast a shadow over the grass. What was the CAUSE of this? a) The sun was rising. b) The grass was cut.

Boxer

COPA Benchmarks

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My body cast a shadow over the grass. What was the CAUSE of this? a) The sun was rising. b) The grass was cut.

Boxer

∃A, B((n1grass(A) ∧ n1sun(B)) ∧ ∃C, D, E((r1over(C, A)∧ (r1Theme(C, D) ∧ (r1Actor(C, E) ∧ (v1cast(C) ∧ (n1shadow(D)∧ (n1body(E) ∧ (r1of(E, D) ∧ n1person(D))))))))∧ ∃F((r1Actor(F, B) ∧ v1rise(F)) ∧ ∃G(r1Theme(G, A) ∧ v1cut(G)))))

COPA Benchmarks

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FO-representation

  • f COPA problem:

∃A, B((n1grass(A) ∧ n1sun(B)) ∧ ∃C, D, E((r1over(C, A)∧ (r1Theme(C, D) ∧ (r1Actor(C, E) ∧ (v1cast(C) ∧ (n1shadow(D)∧ (n1body(E) ∧ (r1of(E, D) ∧ n1person(D))))))))∧ ∃F((r1Actor(F, B) ∧ v1rise(F)) ∧ ∃G(r1Theme(G, A) ∧ v1cut(G)))))

ç√ ç√ ç √ ç √ ç √ ç √ ç √ ç√ ç√ ç√ ç√ ç√ ç√ Background Knowledge: OpenCyc

project(X)

v1cast(D)

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FO-representation

  • f COPA problem:

∃A, B((n1grass(A) ∧ n1sun(B)) ∧ ∃C, D, E((r1over(C, A)∧ (r1Theme(C, D) ∧ (r1Actor(C, E) ∧ (v1cast(C) ∧ (n1shadow(D)∧ (n1body(E) ∧ (r1of(E, D) ∧ n1person(D))))))))∧ ∃F((r1Actor(F, B) ∧ v1rise(F)) ∧ ∃G(r1Theme(G, A) ∧ v1cut(G)))))

WordNet

Bridging Formulae Background Knowledge: OpenCyc

project(X)

v1cast(D)

∀X(v1cast(X) ↔ project(X))

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Hypertableau 1st order

p(z, f(a)) ∧ r(g(a)) → p(x, y) ∨ q((f(x), z)

dom(a) dom(b) . . . p(b, f(a)) q(a, x)) r(g(a))

no backtracking branches can be considered isolated - equality handling! Cade 07

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Hypertableau 1st order

p(z, f(a)) ∧ r(g(a)) → p(x, y) ∨ q((f(x), z)

dom(a) dom(b) . . . p(b, f(a)) q(a, x)) r(g(a))

no backtracking branches can be considered isolated - equality handling! Cade 07

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Hypertableau 1st order

p(z, f(a)) ∧ r(g(a)) → p(x, y) ∨ q((f(x), z)

dom(a) dom(b) . . . p(b, f(a)) q(a, x)) r(g(a))

σ = {z ← b} p(b, f(a)) ∧ r(g(a)) → p(x, y) ∨ q((f(x), b) no backtracking branches can be considered isolated - equality handling! Cade 07

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Hypertableau 1st order

p(z, f(a)) ∧ r(g(a)) → p(x, y) ∨ q((f(x), z)

dom(a) dom(b) . . . p(b, f(a)) q(a, x)) r(g(a))

σ = {z ← b} p(b, f(a)) ∧ r(g(a)) → p(x, y) ∨ q((f(x), b) q(f(x, b) p(x, y) no backtracking branches can be considered isolated - equality handling! Cade 07

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Hypertableau 1st order

p(z, f(a)) ∧ r(g(a)) → p(x, y) ∨ q((f(x), z)

dom(a) dom(b) . . . p(b, f(a)) q(a, x)) r(g(a))

σ = {z ← b} p(b, f(a)) ∧ r(g(a)) → p(x, y) ∨ q((f(x), b) no backtracking branches can be considered isolated - equality handling! Cade 07

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Hypertableau 1st order

p(z, f(a)) ∧ r(g(a)) → p(x, y) ∨ q((f(x), z) π = {x ← a}

dom(a) dom(b) . . . p(b, f(a)) q(a, x)) r(g(a))

σ = {z ← b} p(b, f(a)) ∧ r(g(a)) → p(x, y) ∨ q((f(x), b) no backtracking branches can be considered isolated - equality handling! Cade 07

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Hypertableau 1st order

p(z, f(a)) ∧ r(g(a)) → p(x, y) ∨ q((f(x), z) π = {x ← a}

dom(a) dom(b) . . . p(b, f(a)) q(a, x)) r(g(a))

σ = {z ← b} p(b, f(a)) ∧ r(g(a)) → p(x, y) ∨ q((f(x), b) p(a, y) q(f(a), b) no backtracking branches can be considered isolated - equality handling! Cade 07

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Hypertableau 1st order

p(z, f(a)) ∧ r(g(a)) → p(x, y) ∨ q((f(x), z) π = {x ← a}

dom(a) dom(b) . . . p(b, f(a)) q(a, x)) r(g(a))

σ = {z ← b} p(b, f(a)) ∧ r(g(a)) → p(x, y) ∨ q((f(x), b) p(a, y) q(f(a), b) → dom(a) dom(a) → dom(f(a)) no backtracking branches can be considered isolated - equality handling! Cade 07

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Hypertableau 1st order

p(z, f(a)) ∧ r(g(a)) → p(x, y) ∨ q((f(x), z) π = {x ← a}

dom(a) dom(b) . . . p(b, f(a)) q(a, x)) r(g(a))

σ = {z ← b} p(b, f(a)) ∧ r(g(a)) → p(x, y) ∨ q((f(x), b) p(a, y) q(f(a), b) → dom(a) dom(a) → dom(f(a)) no backtracking branches can be considered isolated - equality handling! Cade 07

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Hyper Tableau My body cast a shadow over the grass. What was the CAUSE of this? a) The sun was rising. b) The grass was cut. ML What is `closer´ to a logical consequence? a) or b)? a)!

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Chinese Room - John Searl Thomas Metzinger

Postbiotic consciousness

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Bernhard Baars

  • Global Workspace Theorie
  • Theatre metapher





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Bernhard Baars

  • Global Workspace Theorie
  • Theatre metapher





  • Consciousness is a gateway to 


vast domains of knowledge 
 and control

  • we can create access to any part 

  • f the brain using consciousness
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Bernhard Baars

  • Global Workspace Theorie
  • Theatre metapher



 „Consciousness may be considered as the gateway to these unconscious sources of knowledge.“

  • Consciousness is a gateway to 


vast domains of knowledge 
 and control

  • we can create access to any part 

  • f the brain using consciousness
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Bernhard Baars

  • Global Workspace Theorie
  • Theatre metapher



 „Consciousness may be considered as the gateway to these unconscious sources of knowledge.“

  • Consciousness is a gateway to 


vast domains of knowledge 
 and control

  • we can create access to any part 

  • f the brain using consciousness

„This is ostensibly based on GWT, but the idea is easily understood without the psycho-babble. The work is very suitable for the AITP workshop.“

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https://www.slideshare.net/alfredoarmella/global-workspace-theory-tutorial

From:

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FOL Formula

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FOL Formula Selection process: Cyc ConceptNet WordNet SInE

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FOL Formula Selection process: Cyc ConceptNet WordNet SInE Background Knowledge

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Hyper FOL Formula Selection process: Cyc ConceptNet WordNet SInE Background Knowledge

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Hyper FOL Formula Selection process: Cyc ConceptNet WordNet SInE Background Knowledge

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Hyper Ground Instances FOL Formula Selection process: Cyc ConceptNet WordNet SInE Background Knowledge

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Hyper Ground Instances FOL Formula Selection process: Cyc ConceptNet WordNet SInE Background Knowledge Hyper’s current thoughts

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Hyper Ground Instances FOL Formula Selection process: Cyc ConceptNet WordNet SInE Background Knowledge Hyper’s current thoughts

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Hyper Ground Instances Selection process: Cyc ConceptNet WordNet SInE Background Knowledge Hyper’s current thoughts

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Hyper Ground Instances Selection process: Cyc ConceptNet WordNet SInE Background Knowledge Hyper’s current thoughts

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Hyper Ground Instances Selection process: Cyc ConceptNet WordNet SInE Background Knowledge Hyper’s current thoughts

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Hyper Ground Instances Selection process: Cyc ConceptNet WordNet SInE Background Knowledge Hyper’s current thoughts

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Hyper Ground Instances Selection process: Cyc ConceptNet WordNet SInE Background Knowledge Hyper’s current thoughts

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Hyper Ground Instances Selection process: Cyc ConceptNet WordNet SInE Background Knowledge Hyper’s current thoughts

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Hyper Ground Instances Selection process: Cyc ConceptNet WordNet SInE Background Knowledge Hyper’s current thoughts

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Hyper Ground Instances Selection process: Cyc ConceptNet WordNet SInE Background Knowledge Hyper’s current thoughts

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Hyper Ground Instances Selection process: Cyc ConceptNet WordNet SInE Background Knowledge Hyper’s current thoughts

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Hyper Ground Instances Selection process: Cyc ConceptNet WordNet SInE Background Knowledge Hyper’s current thoughts

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Hyper Ground Instances Selection process: Cyc ConceptNet WordNet SInE Background Knowledge Hyper’s current thoughts

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Hyper Ground Instances Selection process: Cyc ConceptNet WordNet SInE Background Knowledge Hyper’s current thoughts …

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First Experiments

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First Experiments

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First Experiments

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First Experiments

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todos

what is interesting? (cf. AGInT-System) how to remember? more different knowledge bases