Logic-Based Subsumption Architecture & PERI

1. Logic-Based Subsumption Architecture & PERI

2. Introduction • The LSA is an AI architecture for high-level reasoning and decision-making • Based on Rodney Brooks’ subsumption architecture, where control layers are decomposed in terms of behavior • Uses First Order Logic to describe control of the individual layers • Uses John McCarthy’s circumscription formula for nonmonotonic and commonsense reasoning

3. Brooks-Style Subsumption • The standard model of a robot architecture is a functional model, e.g. sensors → perception → modeling → planning → task recognition → motor control • Subsumption architecture is a behavioral approach, decompose layers in terms of behaviors • Organize layers in order of increasing competence, e.g. avoid objects < wander < explore < build maps < monitor changes < identify objects < plan actions < reason about object behavior • The idea of subsumption is that higher layers depend on lower layers and can also influence their behaviors • Build up on lower layers to create more complex tasks • Layers’ goals can have different priorities in case of conflicting goals

4. Brooks-Style Subsumption • Benefits include: • Have a working robot at the very lowest layer • Decomposition into levels of competence increases ease of testing • Supports additivity, robustness, and high reactivity • Supports concurrency, each layer can have its own processing loop • Because of concurrency and the layer decomposition, layers are independent, so multiple goals can be worked towards simultaneously

5. Brooks-Style Subsumption • Disadvantages • Adding layers increases hardware complexity, so lacks scalability • Semantics of the system unclear • Not declarative, so hard to do higher level reasoning • The next step: Logic-Based Subsumption

6. Logic-Based Subsumption • Layers still decomposed by behaviors • Difference is layer control expressed in FOL, so fully declarative • Layers work concurrently and asynchronously, so are therefore independent • Each layer has its own processing loop and its own theorem prover • Each layer has an axiomatization describing its inputs, outputs, goals, and the relationships between them • A layer has 4 parts – body (contains the axiomatization), sensory and input latches, outputs, and default assumptions

7. Logic-Based Subsumption • Layer structure: (from http://www-formal.stanford.edu/eyal/lsa/) goals

8. Logic-Based Subsumption • Processing Loop: • Collect sensory input and assert as axioms • At the same time, assert inputs from higher layers as axioms • Try to prove the layer’s goal using those axioms and the axioms of the layer’s body • If 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 enough • Does nonmonotonic reasoning using circumscription to handle default assumptions

9. Logic-Based Subsumption • Nonmonotonic reasoning • certain 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 drawn • Models “jumping to conclusions” • Necessary to assert default assumptions, to deal with conflicting goals • Achieves commonsense reasoning • When higher layers draw new conclusions, the old ones are nonmonotonically retracted from lower layers • Accomplished in LSA by John McCarthy’s circumscription formula – allows defaults and gives semantics to the system as a whole

10. Logic-Based Subsumption • Advantages over Brooks-style subsumption: • Fully declarative and described in FOL, so not as hard to do higher level reasoning • Since layers described in FOL: • Very scalable • High applicability • Very extensible

11. The LSA and PERI • The LSA is good for systems that need to do high-level reasoning and/or commonsense reasoning • Speed issues: • Use of nonmonotonic reasoning and layers being independent keeps axiomatizations small therefore proofs small, and also fast enough for real-time control • Proof caching can be done if certain things are proved over and over again, can increase speed • Can add semantic attachments, such as algebraic functions, to parts of layers to improve performance – things that aren’t as easily expressed as theorems • PTTP 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 attachments • Mostly, speed and reactivity depends on the layers’ axiomatizations and how the layers are decomposed

12. The LSA and PERI • Advantages for PERI: • Decomposition of layers in the LSA allows for multiple goals, increased robustness, and concurrency of processes • Concurrency increases speed if wish to do many different things simultaneously • Can build different systems of PERI simultaneously • Since at the lowest layer you have a functional robot (to some degree), testing is easier • The LSA is extensible and can be extended to many different applications • Disadvantages: • defining the different layers and their axiomatizations could be difficult and require a lot of experimentation • Depending on complexity of axiomatizations and the decomposition of layers, may lose some reactivity • How much would this change how PERI is programmed already?