Introducing Chogic: A Primitive Part of
the MARMML Machine Reasoning System
Selmer Bringsjord
Konstantine 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)
Wargaming
 Cracking Project; “Superteaching”
QuickTime™ and a
TIFF (Uncompressed) decompressor
are needed to see this picture.
A while
back,
RPI
Strategic
Investment
hypothesis generation; AI in support of IA
Slate (Intelligence
Analysis)
Item generation
(theorem proving-based
generation)
synthetic characters/psychological time
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
v1.4
• 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.
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 Building
Advanced Synthetic Characters
Same Thing Here:
Definitely Not an Advanced SC!
Every behavior that happens in
The 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 incompleteness
results imply that minds are
superior to all machines?
...
Enough on the RAIR Lab...
What about MARMML/Chogic?
The Lay of the Land
MARMML
(incl. Chogic, ...)
Jon Barwise’s
vision (see e.g.
Hyperproof)
Vampire
Heterogenous reasoning
system built in significant
part on top of Athena
Athena
Spass
The central system
...
Fast and “dirty”
ATPs and
countermodel
generators
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 of
Homo 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
T
T
F
(2) K
T
F
T
{K  A, K} |- A
{K  A, K} |- A
{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
QuickTime™ and a
Animation decompressor
are needed to see this picture.
Sample
Chogic Proof
#2
QuickTime™ and a
Animation decompressor
are needed to see this picture.
THE END