1. 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, 1991. 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 the graph for readability.