Pat Langley School of Computing and Informatics Arizona State University Tempe, Arizona USA Varieties of Problem Solving in a Unified Cognitive Architecture Thanks to D. Choi, T. Konik, U. Kutur, D. Nau, S. Rogers, and D. Shapiro for their many contributions. This talk reports research funded by grants from DARPA IPTO, which is not responsible for its contents.

The I CARUS Architecture I CARUS is a theory of the human cognitive architecture that posits: It shares the assumptions with other cognitive architectures like Soar (Laird et al., 1987) and ACT-R (Anderson, 1993). 1.Short-term memories are distinct from long-term stores 2.Memories contain modular elements cast as symbolic structures 3.Long-term structures are accessed through pattern matching 4.Cognition occurs in retrieval/selection/action cycles 5.Learning involves monotonic addition of elements to memory 6.Learning is incremental and interleaved with performance

Distinctive Features of I CARUS However, I CARUS also makes assumptions that distinguish it from these architectures: Some of these tenets also appear in Bonasso et al.s (2003) 3T, Freeds APEX, and Sun et al.s (2001) CLARION. 1.Cognition is grounded in perception and action 2.Categories and skills are separate cognitive entities 3.Short-term elements are instances of long-term structures 4.Inference and execution are more basic than problem solving 5.Skill/concept hierarchies are learned in a cumulative manner

Cascaded Integration in I CARUS I CARUS adopts a cascaded approach to integration in which lower-level modules produce results for higher-level ones. conceptual inference skill execution problem solving learning Like other unified cognitive architectures, I CARUS incorporates a number of distinct modules.

I CARUS Memories and Processes Long-TermConceptualMemory Short-TermBeliefMemory Short-Term Goal Memory ConceptualInference SkillExecution Perception Environment PerceptualBuffer Problem Solving Skill Learning MotorBuffer Skill Retrieval and Selection Long-Term Skill Memory

Each concept is defined in terms of other concepts and/or percepts. Each skill is defined in terms of other skills, concepts, and percepts. I CARUS interleaves its long-term memories for concepts and skills. Hierarchical Structure of Memory concepts skills

I CARUS interleaves its long-term memories for concepts and skills. Hierarchical Structure of Memory Each concept is defined in terms of other concepts and/or percepts. Each skill is defined in terms of other skills, concepts, and percepts. concepts skills

Basic I CARUS Processes concepts skills Concepts are matched bottom up, starting from percepts. Skill paths are matched top down, starting from intentions. I CARUS matches patterns to recognize concepts and select skills.

I CARUS Interleaves Execution and Problem Solving Executed plan Problem ? Skill Hierarchy Primitive Skills Reactive Execution impasse? Problem Solving yes no This organization reflects the psychological distinction between automatized and controlled behavior.

Means-Ends Problem Solving in I CARUS Solve(G) Push the goal literal G onto the empty goal stack GS. On each cycle, If the top goal G of the goal stack GS is satisfied, Then pop GS. Else if the goal stack GS does not exceed the depth limit, Let S be the skill instances whose heads unify with G. If any applicable skill paths start from an instance in S, Then select one of these paths and execute it. Else let M be the set of primitive skill instances that have not already failed in which G is an effect. If the set M is nonempty, Then select a skill instance Q from M. Push the start condition C of Q onto goal stack GS. Else if G is a complex concept with the unsatisfied subconcepts H and with satisfied subconcepts F, Then if there is a subconcept I in H that has not yet failed, Then push I onto the goal stack GS. Else pop G from the goal stack GS and store information about failure with G's parent. Else pop G from the goal stack GS. Store information about failure with G's parent. Else if G is a complex concept with the unsatisfied subconcepts H and with satisfied subconcepts F, Then if there is a subconcept I in H that has not yet failed, Then push I onto the goal stack GS. Else pop G from the goal stack GS and store information about failure with G's parent. Else pop G from the goal stack GS. Store information about failure with G's parent. Previous versions of I CARUS have used means-ends analysis, which has been observed repeatedly in humans, but it differs from most versions in that it interleaves backward chaining with execution.

A Successful Means-Ends Trace (ontable A T) (on B A) (on C B) (hand-empty) (clear C) (unst. C B) (unstack C B) (clear B) (putdown C T) (unst. B A) (unstack B A) (clear A) (holding C)(hand-empty) (holding B) A B CB A C initial state goal

Problem Solving as Iterative Sampling However, in some domains, humans carry out forward-chaining search with methods like progressive deepening (de Groot, 1978). In response, we have added a new module to I CARUS that: performs mental simulation of a single trajectory consistent with its stored hierarchical skills; performs mental simulation of a single trajectory consistent with its stored hierarchical skills; repeats this process to find a number of alternative paths from the same initial state; repeats this process to find a number of alternative paths from the same initial state; selects the path that produces the best outcome to determine the next primitive skill to execute. selects the path that produces the best outcome to determine the next primitive skill to execute. We refer to this memory-limited search method as hierarchical iterative sampling (Langley, 1992).

More on Iterative Sampling Our initial version of forward search makes a few implausible psychological assumptions: stochastic path selection and final choices are based on reachability heuristics from the AI planning literature; stochastic path selection and final choices are based on reachability heuristics from the AI planning literature; parameters determine the depth of search and number of iterations, rather than memory capacity and time available; parameters determine the depth of search and number of iterations, rather than memory capacity and time available; no progressive deepening occurs when two alternatives produce similar scores. no progressive deepening occurs when two alternatives produce similar scores. Nevertheless, it seems a promising first step toward modeling heuristic search in domains like chess.

Unifying Forward and Backward Search A key question concerns when humans carry out means-ends analysis vs. forward search; some candidate hypotheses are: they use backward chaining except when the branching factor from the goal becomes too large, as in most games; they use backward chaining except when the branching factor from the goal becomes too large, as in most games; they favor backward chaining when goals are very specific and forward search for less constrained goals; they favor backward chaining when goals are very specific and forward search for less constrained goals; they prefer backward chaining but fall back on forward search when they retrieve no relevant skills (Jones & Langley, 2006). they prefer backward chaining but fall back on forward search when they retrieve no relevant skills (Jones & Langley, 2006). We need detailed psychological studies to select among these alternatives or replace them with better ones. Once answered, we can incorporate the results into I CARUS to offer a unified theory of human problem solving.

Contributions of the Research includes hierarchical memories for concepts and skills; includes hierarchical memories for concepts and skills; interleaves conceptual inference with reactive execution; interleaves conceptual inference with reactive execution; resorts to problem solving when it lacks relevant skills; resorts to problem solving when it lacks relevant skills; carries out both means-ends analysis and forward search. carries out both means-ends analysis and forward search. I CARUS is a unified theory of the cognitive architecture that: The latter each account for some aspects of human problem solving, but not for when to invoke each method. Explaining this choice should be a high priority for future work. For more information about the I CARUS architecture, see:

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I CARUS Concepts for In-City Driving ((in-rightmost-lane ?self ?clane) :percepts ((self ?self) (segment ?seg) :percepts ((self ?self) (segment ?seg) (line ?clane segment ?seg)) :relations ((driving-well-in-segment ?self ?seg ?clane) :relations ((driving-well-in-segment ?self ?seg ?clane) (last-lane ?clane) (not (lane-to-right ?clane ?anylane)))) ((driving-well-in-segment ?self ?seg ?lane) :percepts ((self ?self) (segment ?seg) (line ?lane segment ?seg)) :percepts ((self ?self) (segment ?seg) (line ?lane segment ?seg)) :relations ((in-segment ?self ?seg) (in-lane ?self ?lane) :relations ((in-segment ?self ?seg) (in-lane ?self ?lane) (aligned-with-lane-in-segment ?self ?seg ?lane) (centered-in-lane ?self ?seg ?lane) (steering-wheel-straight ?self))) ((in-lane ?self ?lane) :percepts ((self ?self segment ?seg) (line ?lane segment ?seg dist ?dist)) :percepts ((self ?self segment ?seg) (line ?lane segment ?seg dist ?dist)) :tests ((> ?dist -10) ( ?dist -10) (<= ?dist 0)))

Representing Short-Term Beliefs/Goals (current-street me A)(current-segment me g550) (lane-to-right g599 g601)(first-lane g599) (last-lane g599)(last-lane g601) (at-speed-for-u-turn me)(slow-for-right-turn me) (steering-wheel-not-straight me)(centered-in-lane me g550 g599) (in-lane me g599)(in-segment me g550) (on-right-side-in-segment me)(intersection-behind g550 g522) (building-on-left g288)(building-on-left g425) (building-on-left g427)(building-on-left g429) (building-on-left g431)(building-on-left g433) (building-on-right g287)(building-on-right g279) (increasing-direction me)(buildings-on-right g287 g279)

((in-rightmost-lane ?self ?line) :percepts ((self ?self) (line ?line)) :percepts ((self ?self) (line ?line)) :start ((last-lane ?line)) :start ((last-lane ?line)) :subgoals ((driving-well-in-segment ?self ?seg ?line))) :subgoals ((driving-well-in-segment ?self ?seg ?line))) ((driving-well-in-segment ?self ?seg ?line) :percepts ((segment ?seg) (line ?line) (self ?self)) :percepts ((segment ?seg) (line ?line) (self ?self)) :start ((steering-wheel-straight ?self)) :start ((steering-wheel-straight ?self)) :subgoals ((in-segment ?self ?seg) :subgoals ((in-segment ?self ?seg) (centered-in-lane ?self ?seg ?line) (aligned-with-lane-in-segment ?self ?seg ?line) (steering-wheel-straight ?self))) ((in-segment ?self ?endsg) :percepts ((self ?self speed ?speed) (intersection ?int cross ?cross) :percepts ((self ?self speed ?speed) (intersection ?int cross ?cross) (segment ?endsg street ?cross angle ?angle)) :start ((in-intersection-for-right-turn ?self ?int)) :start ((in-intersection-for-right-turn ?self ?int)) :actions (( steer 1))) :actions (( steer 1))) I CARUS Skills for In-City Driving

Directions for Future Research progressive deepening in forward-chaining search progressive deepening in forward-chaining search graded nature of categories and category learning graded nature of categories and category learning model-based character of human reasoning model-based character of human reasoning persistent but limited nature of short-term memories persistent but limited nature of short-term memories creating perceptual chunks to reduce these limitations creating perceptual chunks to reduce these limitations storing and retrieving episodic memory traces storing and retrieving episodic memory traces Future work on I CARUS should incorporate other ideas about: These additions will increase further I CARUS debt to psychology. For more details, see: