Introducing Chogic: A Primitive Part ofthe MARMML Machine Reasoning System

Selmer BringsjordKonstantine Arkoudas, Josh Taylor, Yingrui Yang, Paul Bello

Rensselaer AI & Reasoning (RAIR) Laboratory

Department of Cognitive Science

Department of Computer Science

Department of Decision Sciences & Engineering Systems

Rensselaer Polytechnic Institute (RPI)

Troy NY 12180 USA

eCAP Pavia, Italy 6.04

The Rensselaer AI & Reasoning Lab(The RAIR Lab)

A while back,RPI StrategicInvestment

Cracking Project; “Superteaching”

Slate (IntelligenceAnalysis)

Item generation(theorem proving-basedgeneration)

synthetic characters/psychological time

Wargaming

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hypothesis generation; AI in support of IA

The Paradox of Human vs. Machine Reasoning

• On the one hand, machine reasoners are getting faster, and can do some impressive things.

• On the other hand, as Herb Simon, one of the grandfathers of AI, admitted @ CAP@CMU shortly before he died, machine reasoning is absolutely nowhere when stacked against first-rate human reasoning.

Next-Generation Logic-based AI

• Isolate and dissect human ingenuity.(psychology of reasoning)

• Mathematize this ingenuity courtesy of advanced logical systems.• Implement this ingenuity in working programs.• Augment the ingenuity with machine-specific power.

NGLAI in Support of Intelligence Analysis:Slate

• Reflects new formal theories of hypothesis generation.– E.g., retrospective and

prospective MMOI-based abduction

• Includes a system for sketching out and testing visual arguments

• Designed to model not just deduction, but abduction, induction, and “mental model”-based reasoning.

v1.4

NGLAI for Robotics:PERI

(Psychometric Experimental Robotic Intelligence)

• Scorbot-ER IX

• Sony B&W XC55 Video Camera

• Cognex MVS-8100M Frame Grabber

• Dragon Naturally Speaking Software

• NL (CARMEL & RealPro?)

• BH8-260 BarrettHand Dexterous 3-Finger Grasper System

NGLAI for BuildingAdvanced Synthetic Characters

Where’s the cognition?

Same Thing Here:Definitely Not an Advanced SC!

Every behavior that happens inThe Sims is computed from a number(1- 10) for each attribute.

RASCALS

Define Evil (Philosophy);Build E (NGLAI)

(Neil’s father in Dead Poet’s Society)

NGLAI & The Foundations of AI/Cog Sci

Are people computers? Hypercomputers?Do Gödelian incompletenessresults imply that minds aresuperior to all machines?...

Enough on the RAIR Lab...

What about MARMML/Chogic?

The Lay of the Land

MARMML(incl. Chogic, ...)

Athena

Vampire Spass ...

Fast and “dirty”ATPs and countermodelgenerators

The central system

Heterogenous reasoning system built in significant part on top of Athena

Jon Barwise’s vision (see e.g. Hyperproof)

MARMML Reflects a Turn to the Human Side, where we mine six distinguishing attributes…

1 Resolution? No. Natural Deduction

2 Always expressed in a formal language? No. Natural Language (e.g., English)

MARMML: Multi-Agent Reasoning and Mental MetaLogic

MARMML moves out in four dimensions revealed by an honest, systematic study of the best of human reasoning:

3 Mode: traditional syntactic proofs, exclusively semantic/visual proofs, and proofs that synthesize the two in “hybrid” reasoning (based on MML theory)

4 Type: deductive, inductive, “creative,” “narratological”/abductive

5 Expressivity (syntactic and semantic): propositional, first-order, second-order, …, higher-order, modal, temporal, etc.; and ever more expressive modeling. Wargaming, inevitably, involves a heterogeneous mixing of modal, temporal, deontic, doxastic, deontic operators! What system in the world can do that?

6 Logical Levels (multi-agent reasoning): Agent 2 can evaluate and refute Agent 1’s object-level proof with meta-proof P’; Agent 3 can evaluate and refute P’ with meta-meta-proof P’’, etc.

Denotational Proof Languages (DPLs)

• DPLs are languages for writing proofs and proof tactics in arbitrary logics

• Novel syntax and semantics (based on the abstraction on assumption bases) ensure:– Readability and writability

– Efficient proof checking

– Guaranteed soundness

– Powerful mechanisms for expressing complex proof tactics and tacticals

Wide applicability

• DPLs have been designed and implemented for:– Classical logics (both first- and higher-order)– Intuitionist logics– Modal and temporal logics– Program logics (Hoare-Floyd logics)– Type systems

Athena

• A DPL for classical first-order logic

• Uses natural deduction

• Incorporates a higher-order functional programming language with algebraic data types

• Supports induction, recursion, pattern matching

• Other logics (e.g. modal logic) can be rapidly prototyped by implementing them on top of Athena

Problem 1 for Some Members ofHomo Sapiens Sapiens

If one of the following assertions is true then so is the other:

(1) There is a king in the hand if and only if there is an ace in the hand.

(2) There is a king in the hand.

Which is more likely to be in the hand, if either: the king or the ace?

Solution

You can obviously prove K & A in the cases where

(1) K A (2) K T T {K A, K} |- A T F {K A, K} |- A F T {K A, K} |- A so everything must boil down to the F F case. It's easy here to do a proof that can get A (constructive dilemma and reductio), but ~K instead of K. Ergo, the answer is A.

King/Ace Proofs

Sample Chogic Proof #1

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Sample Chogic Proof

#2

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THE END