Concurrent Inference Graphs Daniel R. Schlegel Department of Computer Science and Engineering Problem Summary Inference graphs 2 in their current form only support propositional logic. We expand it to support L A – A Logic of Arbitrary and Indefinite Objects. 3 Note: Much of this is work in progress, advice and criticism are very welcome! This work has been supported by a Multidisciplinary University Research Initiative (MURI) grant (Number W911NF-09- 1-0392) for Unified Research on Network-based Hard/Soft Information Fusion, issued by the US Army Research Office (ARO) under the program management of Dr. John Lavery. Inference Components Enhanced Channels • Channels appear not only within a rule, but also from rule consequents to unifiable rule antecedents, and from consequents to unifiable questions. • When formulas are added to the graph, the are unified with all others using a kind of substitution tree 1 . • Channels (and inference segments) are extended to contain: • Verifiers – Verify substitution is applicable. • Switches – Changes variable context. • Valves – Prevent or allow substitutions to pass through. Example: Subsumption Inference References 1.Hoder, K., & Voronkov, A. Comparing unification algorithms in first-order theorem proving. In KI 2009: Advances in Artificial Intelligence (pp. 435-443). Springer Berlin Heidelberg, 2009. 2.Schlegel, D. R. & Shapiro, S. C. Concurrent Reasoning with Inference Graphs. In Proceedings of the Third International IJCAI Workshop on Graph Structures for Knowledge Representation and Reasoning (GKR 2013), 2013, in press. 3.Shapiro, S. C. A Logic of Arbitrary and Indefinite Objects. In D. Dubois, C. Welty, & M. Williams, Principles of Knowledge Representation and Reasoning: Proceedings of the Ninth International Conference (KR2004), AAAI Press, Menlo Park, CA, 2004, 565-575. 4.Woods, W. A. Understanding subsumption and taxonomy. In Sowa, J., ed., Principles of Semantic Networks. Los Altos, CA: Morgan Kaufmann. 45–94, Draws influences from: • RETE Networks • Alpha Networks • Beta Networks • Terminal Node • Token • Truth Maintenance Systems • LATMS Constraints • LTMS Node • Active Connection Graphs • Report • Filter • Switch • P-Tree • S-Index • p-node Some of these components are, in many ways, equivalent: • ACG Report = RETE Token • “Message” • Beta Network = P-Tree • “Binary Conjunct Tree” • “Chain” of Alpha Network = ACG Filter • “Verifier” • Terminal Node = LATMS Constraint = ACG Rule Node • “Rule Node” • LTMS Node = p-node • “Propositional Node” From MGU factorization L A – A Logic of Arbitrary and Indefinite Objects • A logic designed by Stuart C. Shapiro for: • KRR Systems • NL Understanding / Generation • Commonsense Reasoning • Uses arbitrary/indefinite terms, not universally/existentially quantified variables. • Structure sharing between terms. • Makes term subsumption possible. Example (Structure Sharing): The arbitrary domesticated dog is both loyal and friendly. Notice that only one arbitrary domesticated dog has been created in the graph. CSNePS will support at least 2 types of subsumption. 4 • Structural Subsumption: by their formal definitions, C1 is more general than C2. • Example: Since the arbitrary domesticated dog is friendly, the arbitrary white domesticated dog is friendly. • Recorded Subsumption: C1 is above C2 in a subsumption data structure. • Example: If the arbitrary Animal is alive, then according to this hierarchy, so are any Dogs, Huskies, or Cats – including the arbitrary ones. • Example: The property of having two different colored eyes (which a Husky has) would not be inherited by Dog. • The type hierarchy used in recorded subsumption works in concert with unification, to limit unifiers. • What (if any) types of deduced subsumption are possible is still under consideration. Belief revision is a complicating factor. This graph contains the proposition that every arbitrary entity is friends with their arbitrary child. It also contains the wh-question “Who is Dave friends with?” Two i- channels are created from wft1 to wft3, since the friends relation is symmetric. Note that arb1, arb2, qvar1, and Dave are all entities, but that data has been omitted from