Stream Reasoning using Temporal Logic and Predictive Probabilistic - PowerPoint PPT Presentation

Stream Reasoning using Temporal Logic and Predictive Probabilistic State Models Mattias Tiger Fredrik Heintz Artificial Intelligence and Integrated Computer Systems Department of Computer and Information Science Link¨ oping University, Sweden

Introduction Stochastic and Predictive Stream Reasoning Motivation UAV example Stream Reasoning Summary Execution Monitoring in Robotics Am I in a no-fly zone? - boolean Is it likely that I am in a no-fly zone? Is it likely that I am about to crash into the wall in the near future? Mattias Tiger, Fredrik Heintz Link¨ oping University 2/13

Introduction Stochastic and Predictive Stream Reasoning Motivation UAV example Stream Reasoning Summary Execution Monitoring in Robotics Am I in a no-fly zone? - boolean Is it likely that I am in a no-fly zone? Is it likely that I am about to crash into the wall in the near future? Mattias Tiger, Fredrik Heintz Link¨ oping University 2/13

Introduction Stochastic and Predictive Stream Reasoning Motivation UAV example Stream Reasoning Summary Metric Temporal Logic ( MTL ) formulas are evaluated over the stream (infinite state sequence) using Progression . Incremental evaluation by formula re-writing to incorporate what has been observed so far. Mattias Tiger, Fredrik Heintz Link¨ oping University 3/13

Introduction Intuition Stochastic and Predictive Stream Reasoning P-MTL: Stochastic temporal term operator UAV example P-MTL: Syntax Summary P-MTL: Grounding What do we know (about terms) at t k ? Mattias Tiger, Fredrik Heintz Link¨ oping University 4/13

Introduction Intuition Stochastic and Predictive Stream Reasoning P-MTL: Stochastic temporal term operator UAV example P-MTL: Syntax Summary P-MTL: Grounding What do we know (about terms) at t k ? Mattias Tiger, Fredrik Heintz Link¨ oping University 5/13

Introduction Intuition Stochastic and Predictive Stream Reasoning P-MTL: Stochastic temporal term operator UAV example P-MTL: Syntax Summary P-MTL: Grounding What do we know (about terms) at t k ? Mattias Tiger, Fredrik Heintz Link¨ oping University 5/13

Introduction Intuition Stochastic and Predictive Stream Reasoning P-MTL: Stochastic temporal term operator UAV example P-MTL: Syntax Summary P-MTL: Grounding What do we know (about terms) at t k ? Mattias Tiger, Fredrik Heintz Link¨ oping University 5/13

Introduction Intuition Stochastic and Predictive Stream Reasoning P-MTL: Stochastic temporal term operator UAV example P-MTL: Syntax Summary P-MTL: Grounding What do we know (about terms) at t k ? Mattias Tiger, Fredrik Heintz Link¨ oping University 5/13

Introduction Intuition Stochastic and Predictive Stream Reasoning P-MTL: Stochastic temporal term operator UAV example P-MTL: Syntax Summary P-MTL: Grounding Truth values of predicates Numerical values of terms Stochastic estimates of terms (Green, solid outline) Stochastic predictions of terms (Red, dashed outline) Mattias Tiger, Fredrik Heintz Link¨ oping University 6/13

Introduction Intuition Stochastic and Predictive Stream Reasoning P-MTL: Stochastic temporal term operator UAV example P-MTL: Syntax Summary P-MTL: Grounding An alternative view Mattias Tiger, Fredrik Heintz Link¨ oping University 7/13

Introduction Intuition Stochastic and Predictive Stream Reasoning P-MTL: Stochastic temporal term operator UAV example P-MTL: Syntax Summary P-MTL: Grounding P-MTL is MTL extended with a stochastic temporal term operator Estimated feature: t | t Altitude[ uav1 ] ( t ≤ 0) t ′ | t Altitude[ uav1 ] ( t ≤ 0 , t ′ � = t ) Predicted feature: � � Altitude[ uav1 ] − Altitude[ roofA ]) > 2 � � Pr (( 0 | 0 Altitude[ uav1 ] − 0 | 0 Altitude[ roofA ]) > 2) ≥ 0 . 99 � � Pr (( 3 | 0 Altitude[ uav1 ] − 0 | 0 Altitude[ roofA ]) > 2) ≥ 0 . 99 Mattias Tiger, Fredrik Heintz Link¨ oping University 8/13

Introduction Intuition Stochastic and Predictive Stream Reasoning P-MTL: Stochastic temporal term operator UAV example P-MTL: Syntax Summary P-MTL: Grounding P-MTL is MTL extended with a stochastic temporal term operator Estimated feature: t | t Altitude[ uav1 ] ( t ≤ 0) t ′ | t Altitude[ uav1 ] ( t ≤ 0 , t ′ � = t ) Predicted feature: � � Altitude[ uav1 ] − Altitude[ roofA ]) > 2 � � Pr (( 0 | 0 Altitude[ uav1 ] − 0 | 0 Altitude[ roofA ]) > 2) ≥ 0 . 99 � � Pr (( 3 | 0 Altitude[ uav1 ] − 0 | 0 Altitude[ roofA ]) > 2) ≥ 0 . 99 Mattias Tiger, Fredrik Heintz Link¨ oping University 8/13

Introduction Intuition Stochastic and Predictive Stream Reasoning P-MTL: Stochastic temporal term operator UAV example P-MTL: Syntax Summary P-MTL: Grounding P-MTL is MTL extended with a stochastic temporal term operator Estimated feature: t | t Altitude[ uav1 ] ( t ≤ 0) t ′ | t Altitude[ uav1 ] ( t ≤ 0 , t ′ � = t ) Predicted feature: � � Altitude[ uav1 ] − Altitude[ roofA ]) > 2 � � Pr (( 0 | 0 Altitude[ uav1 ] − 0 | 0 Altitude[ roofA ]) > 2) ≥ 0 . 99 � � Pr (( 3 | 0 Altitude[ uav1 ] − 0 | 0 Altitude[ roofA ]) > 2) ≥ 0 . 99 Mattias Tiger, Fredrik Heintz Link¨ oping University 8/13

Introduction Intuition Stochastic and Predictive Stream Reasoning P-MTL: Stochastic temporal term operator UAV example P-MTL: Syntax Summary P-MTL: Grounding P-MTL is MTL extended with a stochastic temporal term operator Estimated feature: t | t Altitude[ uav1 ] ( t ≤ 0) t ′ | t Altitude[ uav1 ] ( t ≤ 0 , t ′ � = t ) Predicted feature: � � Altitude[ uav1 ] − Altitude[ roofA ]) > 2 � � Pr (( 0 | 0 Altitude[ uav1 ] − 0 | 0 Altitude[ roofA ]) > 2) ≥ 0 . 99 � � Pr (( 3 | 0 Altitude[ uav1 ] − 0 | 0 Altitude[ roofA ]) > 2) ≥ 0 . 99 Mattias Tiger, Fredrik Heintz Link¨ oping University 8/13

Introduction Intuition Stochastic and Predictive Stream Reasoning P-MTL: Stochastic temporal term operator UAV example P-MTL: Syntax Summary P-MTL: Grounding P-MTL is MTL extended with a stochastic temporal term operator Estimated feature: t | t Altitude[ uav1 ] ( t ≤ 0) t ′ | t Altitude[ uav1 ] ( t ≤ 0 , t ′ � = t ) Predicted feature: � � Altitude[ uav1 ] − Altitude[ roofA ]) > 2 � � Pr (( 0 | 0 Altitude[ uav1 ] − 0 | 0 Altitude[ roofA ]) > 2) ≥ 0 . 99 � � Pr (( 3 | 0 Altitude[ uav1 ] − 0 | 0 Altitude[ roofA ]) > 2) ≥ 0 . 99 Mattias Tiger, Fredrik Heintz Link¨ oping University 8/13

Introduction Intuition Stochastic and Predictive Stream Reasoning P-MTL: Stochastic temporal term operator UAV example P-MTL: Syntax Summary P-MTL: Grounding Predicates P ( τ 1 , . . . , τ n ) | ¬ α | α ∧ β | α ∨ β | α → β | t 1 α | [ t 1 , t 2 ] α | α | [ t 1 , t 2 ] α | α Terms ¯ t 1 ¯ t 1 | t 2 ¯ f [ const ] | f [ const ] | f [ const ] | const | f ( τ 1 , . . . , τ n ) | Pr ( g ( τ p , c 1 , . . . , c m )) Mattias Tiger, Fredrik Heintz Link¨ oping University 9/13

Introduction Intuition Stochastic and Predictive Stream Reasoning P-MTL: Stochastic temporal term operator UAV example P-MTL: Syntax Summary P-MTL: Grounding Grounding of P-MTL terms in computational environment Mattias Tiger, Fredrik Heintz Link¨ oping University 10/13

Introduction Intuition Stochastic and Predictive Stream Reasoning P-MTL: Stochastic temporal term operator UAV example P-MTL: Syntax Summary P-MTL: Grounding Grounding of P-MTL terms in computational environment E = � T , O , F , ¯ F , X , D , T , P� Mattias Tiger, Fredrik Heintz Link¨ oping University 10/13

Introduction Stochastic and Predictive Stream Reasoning UAV example Summary Example: Execution Monitoring A UAV may only move under the conditions that Its perception is precise The estimate of its position to be within a 1m radius circle with 99% probability Its near-time predictions are precise The prediction of its position 3 seconds from now must be within a 1m radius circle with 95% probability Its near-time prediction quality is high The prediction must match with the then estimated position with at least 50% similarity. Mattias Tiger, Fredrik Heintz Link¨ oping University 11/13

Introduction Stochastic and Predictive Stream Reasoning UAV example Summary Example: Execution Monitoring A UAV may only move under the conditions that Its perception is precise The estimate of its position to be within a 1m radius circle with 99% probability Its near-time predictions are precise The prediction of its position 3 seconds from now must be within a 1m radius circle with 95% probability Its near-time prediction quality is high The prediction must match with the then estimated position with at least 50% similarity. Mattias Tiger, Fredrik Heintz Link¨ oping University 11/13

Introduction Stochastic and Predictive Stream Reasoning UAV example Summary Example: Execution Monitoring A UAV may only move under the conditions that Its perception is precise The estimate of its position to be within a 1m radius circle with 99% probability Its near-time predictions are precise The prediction of its position 3 seconds from now must be within a 1m radius circle with 95% probability Its near-time prediction quality is high The prediction must match with the then estimated position with at least 50% similarity. Mattias Tiger, Fredrik Heintz Link¨ oping University 11/13