Logic-Based Subsumption Architecture & PERI

IntroductionThe LSA is an AI architecture for high-level reasoning and decision-makingBased on Rodney Brooks subsumption architecture, where control layers are decomposed in terms of behaviorUses First Order Logic to describe control of the individual layersUses John McCarthys circumscription formula for nonmonotonic and commonsense reasoning

Brooks-Style SubsumptionThe standard model of a robot architecture is a functional model, e.g. sensors perception modeling planning task recognition motor controlSubsumption architecture is a behavioral approach, decompose layers in terms of behaviorsOrganize layers in order of increasing competence, e.g. avoid objects < wander < explore < build maps < monitor changes < identify objects < plan actions < reason about object behaviorThe idea of subsumption is that higher layers depend on lower layers and can also influence their behaviorsBuild up on lower layers to create more complex tasksLayers goals can have different priorities in case of conflicting goals

Brooks-Style SubsumptionBenefits include:Have a working robot at the very lowest layerDecomposition into levels of competence increases ease of testingSupports additivity, robustness, and high reactivitySupports concurrency, each layer can have its own processing loopBecause of concurrency and the layer decomposition, layers are independent, so multiple goals can be worked towards simultaneously

Brooks-Style SubsumptionDisadvantagesAdding layers increases hardware complexity, so lacks scalabilitySemantics of the system unclearNot declarative, so hard to do higher level reasoning

The next step: Logic-Based Subsumption

Logic-Based SubsumptionLayers still decomposed by behaviorsDifference is layer control expressed in FOL, so fully declarativeLayers work concurrently and asynchronously, so are therefore independentEach layer has its own processing loop and its own theorem proverEach layer has an axiomatization describing its inputs, outputs, goals, and the relationships between themA layer has 4 parts body (contains the axiomatization), sensory and input latches, outputs, and default assumptions

Logic-Based SubsumptionLayer structure:(from http://www-formal.stanford.edu/eyal/lsa/)goals

Logic-Based SubsumptionProcessing Loop:Collect sensory input and assert as axiomsAt the same time, assert inputs from higher layers as axiomsTry to prove the layers goal using those axioms and the axioms of the layers bodyIf goal proved, transmit goal to lower layer (at lowest layer, transmit to robot manipulators)Proof depth limit used if goal cannot be proven or proven efficiently enoughDoes nonmonotonic reasoning using circumscription to handle default assumptions

Logic-Based SubsumptionNonmonotonic reasoningcertain conclusions can be drawn with a certain set of premises, but if a different premise is added to that set, the same conclusions may or may not be drawnModels jumping to conclusionsNecessary to assert default assumptions, to deal with conflicting goalsAchieves commonsense reasoningWhen higher layers draw new conclusions, the old ones are nonmonotonically retracted from lower layersAccomplished in LSA by John McCarthys circumscription formula allows defaults and gives semantics to the system as a whole

Logic-Based SubsumptionAdvantages over Brooks-style subsumption:Fully declarative and described in FOL, so not as hard to do higher level reasoningSince layers described in FOL:Very scalableHigh applicabilityVery extensible

The LSA and PERIThe LSA is good for systems that need to do high-level reasoning and/or commonsense reasoningSpeed issues:Use of nonmonotonic reasoning and layers being independent keeps axiomatizations small therefore proofs small, and also fast enough for real-time controlProof caching can be done if certain things are proved over and over again, can increase speedCan add semantic attachments, such as algebraic functions, to parts of layers to improve performance things that arent as easily expressed as theoremsPTTP theorem prover used (in Prolog, but available in LISP as well) theorem prover chosen must be fully automated, capable of nonmonotonic reasoning, and capable of adding semantic attachmentsMostly, speed and reactivity depends on the layers axiomatizations and how the layers are decomposed

The LSA and PERIAdvantages for PERI:Decomposition of layers in the LSA allows for multiple goals, increased robustness, and concurrency of processesConcurrency increases speed if wish to do many different things simultaneouslyCan build different systems of PERI simultaneouslySince at the lowest layer you have a functional robot (to some degree), testing is easierThe LSA is extensible and can be extended to many different applicationsDisadvantages:defining the different layers and their axiomatizations could be difficult and require a lot of experimentationDepending on complexity of axiomatizations and the decomposition of layers, may lose some reactivityHow much would this change how PERI is programmed already?

notes