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A Production Rule-Based Framework for Causal and Epistemic Reasoning
Theodore Patkos, Abdelghani Chibani, Dimitris Plexousakis, Yacine Amirat ({patkos, chibani, amirat}@u-pec.fr, [email protected])
Laboratoire Images Signaux et Systèmes Intelligents (LISSI) University of Paris-Est Creteil, Paris
Institute of Computer Science –
Foundation for Research and Technology Hellas (FO.R.T.H.)
6th International Symposium on Rules (RuleML’12),
Research Work supported by the ITEA 2 EU Projects: A2NETS, PREDYKOT
Outline
• Overview
• (Epistemic) Action Theories
• Production Rule-based Framework
• Application Domain
• Conclusions
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Motivation and Objectives
• Action theories and production systems have widely been used in KR&R to represent knowledge change in dynamic domains.
• Our objective is to exploit the expressive capacity of logic-based theories and the efficiency of rule-based systems, reconciling their differences.
• The outcome is a complete framework that performs runtime reasoning about events, knowledge and time in expressive domains.
• The system can carry out temporal projection and deductive narrative verification tasks and is evaluated in real-world settings
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Framework overview
Event Calculus • Reasoning about action and time • Solution to problems (frame,
ramification, qualification) • Commonsense phenomena
DECKT • Epistemic reasoning • Hidden causal dependencies, rather
than possible worlds structures • Sensing, potential actions etc
Rule-based forward-chaining production system
• NaF, semi-destructive update • Salience values, subsumption…
• Online/offline reasoning • Multiple model
generation • GUI/Java interface
Application Domain • Ambient Intelligence, AAL • Benchmark problems (e.g.,
Shanahan’s circuit)
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Outline
• Overview
• (Epistemic) Action Theories
• Production Rule-based Framework
• Application Domain
• Conclusions
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Background – Action Theories
• The objective is to express the dynamics of the world
• Therefore always include a more or less implicit general notions of time,
change and causality.
• Action Theories automate the
process of commonsense reasoning, in order to • predict the outcome of a given
action sequence • explain observations • find a situation in which certain
goal conditions are met.
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Background – Commonsense phenomena
• Related issues • Representation • Effects of Events • Indirect Effects of Events (Ramification problem) • Context-dependent Effects • Non-deterministic Effects • Concurrent Events • Preconditions • Inertia (Frame problem) • Actions with duration • Delayed Effects and Continuous Change • Default Reasoning (Qualification problem) • …
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Background – Discrete Time Event Calculus
• The EC distinguishes three kinds of objects – events, fluents and timepoints. To do this, it appeals to a sorted first-order language.
• Commonsense Law of Inertia: things tend to persist unless affected by some event.
Positive and Negative Effect Axioms (Σ)
fi C [HoldsAt(fi,t)] Initiates(e,f,t)
fi C [HoldsAt(fi,t)] Terminates(e,f,t)
State Constraints (Ψ) i [HoldsAt(fi,t)] HoldsAt(f,t)
EC Predicates
• HoldsAt(f,t)
• ReleasedAt(f,t)
• Happens(e,t)
• Initiates(e,f,t)
• Terminates(e,f,t)
• Releases(e,f,t)
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Epistemic Action Theories
• Epistemic (modal) logic: An agent is
said to know a fact if this is true in all possible worlds.
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Epistemic and Causal Reasoning
• Action theories that do not model time explicitly have been extended to reason about knowledge in a straightforward manner. • The Situation Calculus
[Moore 1985, Scherl&Levesque 2003]
• The Fluent Calculus [Thielscher 2000]
• The Action Language Ak [Lobo et al. 2001]
• For example, suppose an action E that makes F true if F’ is true:
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Theodore Patkos et al. 11
DECKT – Hidden Causal Dependencies
• We developed a unified formal theory for epistemic, causal and temporal reasoning
• able to express diverse phenomena of commonsense reasoning, about knowledge
• still being computationally feasible.
E
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Outline
• Overview
• (Epistemic) Action Theories
• Production Rule-based Framework
• Application Domain
• Conclusions
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EC Jess-based Reasoner
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Requirements and Challenges
• There exist different implementations of the Event Calculus for offline reasoning, • but certain of its features are not appropriate for runtime execution
(e.g., explicit frame axioms – computational frame problem)
• DECKT has been designed for practical implementations, • Therefore introduces added features not typically met in Event Calculus
(e.g., reification of formulas, time-dependent meta axioms for handling of HCDs)
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DECKT Time-Dependent Meta-Axioms
fi C [HoldsAt(fi,t)] Initiates(e,f,t)
• Event e initiates f if f’ is true • (KT6.1.1) handles the case of
unknown preconditions
• Circumscription at every timepoint would be inefficient.
e
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Production rules with high level structures
• Features that we employ with rule-based reasoning involve • Dynamic rule construction to accommodate HCDs • Semi-destructive update of the KB, where applicable • NaF, rather than circumscription • List handling • Salience values for conflict resolution (e.g., concurrent events). • Numerical manipulations
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• Released fluents and NaF
Operational semantics – Model generator
Sensing and
Acting
KB
DEC/DECKT axioms (destructive update)
Ramifications (state constraints)
Triggered events
Alternative Models
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Non-Epistemic Reasoning Cycle
KB of Fluents
Released
Released
Released Constrained
Effect axioms
fi C[HoldsAt(fi,t)] Initiates(e,f,t) fi C [HoldsAt(fi,t)] Terminates(e,f,t)
State Constrains
i [HoldsAt(fi,t)] HoldsAt(f,t)
.
.
.
Trigger axioms
.
.
.
.
.
.
fi C [HoldsAt(f1,t)]
Happens(e,t)
Sensing
X
X X
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T=t T=t+1
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Epistemic Reasoning Cycle
KB of Epistemic
Fluents
Effect axioms
State Constrains
Trigger axioms
Sensing
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T=t T=t+1
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An Informal Note on Complexity
• The logical theories set a lower bound as to how efficient an
implementation can be.
• The predominant computational complexity factor… • for the non-epistemic case is the number of released fluents • for the epistemic case is the set of HCDs
• Query answering on ground facts is of linear complexity.
• Jess pattern matching depends on the syntactic form of rules. • Ranges from O(p) to O(pn)
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Framework overview
Event Calculus • Reasoning about action and time • Solution to problems (frame,
ramification, qualification) • Commonsense phenomena
DECKT • Epistemic reasoning • Hidden causal dependencies, rather
than possible worlds structures • Sensing, potential actions etc
Rule-based forward-chaining production system
• NaF, semi-destructive update • Salience values, subsumption…
• Online/offline reasoning • Multiple model
generation • GUI/Java interface
Application Domain • Ambient Intelligence, AAL • Benchmark problems (e.g.,
Shanahan’s circuit)
Th
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tica
l fo
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Imp
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Outline
• Overview
• (Epistemic) Action Theories
• Production Rule-based Framework
• Application Domain
• Conclusions
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Application Domain – Ambient Intelligence and Ubiquitous Robotics
• Sensor-rich collaborative environments
• Temporal constraints are ubiquitous
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Conceptual Layers – Knowledge representation in a smart space
• Moving from low-level data to high-level knowledge inference more expressive tools are needed
• AI has a decisive role to play: • representation of
contextual knowledge, • context inference,
• collaboration of devices to achieve common objectives,
• planning in dynamic domains,
• commonsense reasoning
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High-level Activity Recognition – Challenges for the State-of-the-Art
• Semantic Web tools (ontologies and rule-based reasoning) are widely used
to tackle AmI-related problems
• Complex ambient systems test the limits of these methods in terms of expressiveness and reasoning capacity.
• Agents inhabiting smart spaces need to exhibit • Cognitive skills and commonsense reasoning • Temporal reasoning • Operate under partial observability
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Reactive Reasoning and Temporal Projection
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Outline
• Overview
• (Epistemic) Action Theories
• Production Rule-based Framework
• Application Domain
• Conclusions
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Contributions and Ongoing Work
• The Event Calculus provides a declarative specification of state transitions,
while DECKT provides a Kripke-equivalent epistemic semantics
• Production rules obtain high-level structures.
• We aim at a tool for both educational and practical use.
• We extend the editor to support the full expressive power of the EC
• Benchmark and use case evaluation of real settings is our ongoing work, considering further enhancements of the system
• We study its integration with probabilistic methods of inference.
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The end
Thank you for your attention!