Joshua Taylor Selmer Bringsjord and Andrew Shilliday Rensselaer AI & Reasoning (RAIR) Laboratory

1. Slate: An Intelligent Assistant to Professionals and Students in the fields of Intelligence Analysis, Mathematics, and Logic Joshua Taylor Selmer Bringsjord and Andrew Shilliday Rensselaer AI & Reasoning (RAIR) Laboratory Department of Cognitive Science Department of Computer Science Rensselaer Polytechnic Institute (RPI) Troy NY 12180 US 03.20.05

3. What is Slate? • System for Logical Analysis and Theorem Extraction (SLATE) • A workbench for visual reasoning • A reasoning validity checker • (intelligent) hypothesis generation system • A proof finder * • and much more...

4. What is Slate Not? • A Theorem Prover • A Natural Language Processor • A replacement for human reasoners

5. Professional “Laic” Reasoning Formal Reasoning IAs, item writers, ... Mathematicians, logicians, technical philosophers Students of IA, of item writing, ... Students of math, logic, philosophy For Slate,Two General Uses; Four Specific Ones

6. Parallel (Idealized) Processes? IA tasked. Reads, gathers data, etc. Develops an argument-sketch in support of a hypothesis or recommendation. Fills in gaps and refines the argument. Issues a written report expressing/defending the argument. Mathematician given problem. Reads, gathers info on prior work, etc. Develops a proof-sketch in support of a theorem. Fills in gaps in the sketch. Releases an “informal” proof to the community.

7. Original Concept

8. Current Release: v2.0

9. Some Innovative Features(from among many) • Reflects new formal theories of hypothesis generation. • E.g., retrospective and prospective MMOI-based abduction • Includes a system -- S -- for sketching out and checking visual natural deduction-style arguments • Designed to model not just deduction, but abduction, induction, and “mental model”-based reasoning. • Seamless integration with machine reasoning systems (SNARK, OSCAR, Athena, etc.)

10. System S • A proof creation / validation environment

11. Hypothesis Generation • Simple (naive) • e.g • MMOI • If Agent has motive, means, and opportunity, then generate intent. • Deductive • Abductive

12. Inference-Based Hypothesis Generation some algorithm some inference scheme analyst knowledge (some particular form of deduction, abduction, induction, analogical reasoning, etc.)

13. A Wonderfully RichSet of Options -- Even Under Just the “Deductive” Umbrella (Yes, it’s very naive, and simplistic) Hypotheses = Hypotheses = Hypotheses = . . .

14. But there is overwhelming empirical evidence that humans often reason on the basis of mental models expressed pictographically. One such application to make use of pictographic models: Barwise & Etchemendy’s Hyperproof

15. Model-Based Hypothesis Generation some algorithm some modeling scheme analyst knowledge (see Lindstrom’s Theorem)

16. What the Slate Team is Doing in This Area • Alloy, MACE, SEM, ... everybody lives in their idiosyncratic world. • We have invented MDF, (Model Description Format), a lingua franca (L) for model finding. • We are crafting algorithms that will take models expressed in L and output diagrams with which intelligence analysts will be at home. • Given this, a Slate user can generate hypotheses, in visual, “mental model” form.

17. SNARK Built-in Temporal and spacial reasoning OSCAR Generates natural deduction-style proofs. Otter Fairly fast resolution-based theorem prover Vampire Otter style, with much improved speed SEM a System for Enumerating finite Models (model finder) Paradox a model finder which accepts propositions in TPTP format SPASS another theorem prover (and many more) Theorem Proving

18. The ‘New Order’ Scenario • John H. was killed by a member of the Al-Qaeda cell 'The New Order'. • The only members of 'The New Order' were John H., Majed H., and Essid D. • Within-cell killings only occur when the attacker believes the victim is a traitor, and never when the attacker is of lower rank. • Essid D. believes that nobody is a traitor who John H. believes is a traitor. • John H. believes everyone except Majed H. is a traitor. • Majed H. believes that everyone who is not of lower rank than John H. is a traitor. • Majed H. believes everyone is a traitor who John H. believes is a traitor. • No one believes everyone in 'The New Order' is a traitor. P1 P2 P3 P4 P5 P6 P7

21. Paradox generates this: Which is translated to MDF

22. Neither seems quite as nice as this:

30. A logician might approve of the final proof, but to an untrained reasoner, it’s not much use. We can generate models and show them in an diagram; can we take proofs and make them accessible too??