ASP Solving for Expanding Universes Martin Gebser Tomi Janhunen - PowerPoint PPT Presentation

ASP Solving for Expanding Universes Martin Gebser Tomi Janhunen Holger Jost Roland Kaminski Torsten Schaub Aalto University INRIA Rennes University of Potsdam G, Janhunen, Jost, Kaminski, Schaub ASP Solving for Expanding Universes 1 / 13

Outline 1 Motivation 2 Expanding Logic Programs 3 Conclusions G, Janhunen, Jost, Kaminski, Schaub ASP Solving for Expanding Universes 2 / 13

Motivation Outline 1 Motivation 2 Expanding Logic Programs 3 Conclusions G, Janhunen, Jost, Kaminski, Schaub ASP Solving for Expanding Universes 3 / 13

Motivation Multi-shot Solving Input Output Ground Solve Traditional ASP systems were devised for one-shot solving Modern ASP systems allow for multi-shot solving in a reactive way New properties or objects must be integrated dynamically Due to non-monotonicity, new information can invalidate conclusions flies ( X ) ← bird ( X ) , ∼ penguin ( X ) bird ( tweety ) ← penguin ( tweety ) ← | = { bird ( tweety ) , ¬ penguin ( tweety ) , flies ( tweety ) } General approach to integrate new information into reasoning process? G, Janhunen, Jost, Kaminski, Schaub ASP Solving for Expanding Universes 4 / 13

Motivation Multi-shot Solving Input Output Ground Solve Traditional ASP systems were devised for one-shot solving Modern ASP systems allow for multi-shot solving in a reactive way New properties or objects must be integrated dynamically Due to non-monotonicity, new information can invalidate conclusions flies ( X ) ← bird ( X ) , ∼ penguin ( X ) bird ( tweety ) ← penguin ( tweety ) ← | = { bird ( tweety ) , ¬ penguin ( tweety ) , flies ( tweety ) } General approach to integrate new information into reasoning process? G, Janhunen, Jost, Kaminski, Schaub ASP Solving for Expanding Universes 4 / 13

Motivation Multi-shot Solving Input Output Ground Solve Traditional ASP systems were devised for one-shot solving Modern ASP systems allow for multi-shot solving in a reactive way New properties or objects must be integrated dynamically Due to non-monotonicity, new information can invalidate conclusions flies ( X ) ← bird ( X ) , ∼ penguin ( X ) bird ( tweety ) ← penguin ( tweety ) ← | = { bird ( tweety ) , ¬ penguin ( tweety ) , flies ( tweety ) } General approach to integrate new information into reasoning process? G, Janhunen, Jost, Kaminski, Schaub ASP Solving for Expanding Universes 4 / 13

Motivation Multi-shot Solving Input Output Ground Solve Traditional ASP systems were devised for one-shot solving Modern ASP systems allow for multi-shot solving in a reactive way New properties or objects must be integrated dynamically Due to non-monotonicity, new information can invalidate conclusions flies ( X ) ← bird ( X ) , ∼ penguin ( X ) bird ( tweety ) ← penguin ( tweety ) ← | = { bird ( tweety ) , ¬ penguin ( tweety ) , flies ( tweety ) } General approach to integrate new information into reasoning process? G, Janhunen, Jost, Kaminski, Schaub ASP Solving for Expanding Universes 4 / 13

Motivation Multi-shot Solving Input Output Ground Solve Traditional ASP systems were devised for one-shot solving Modern ASP systems allow for multi-shot solving in a reactive way New properties or objects must be integrated dynamically Due to non-monotonicity, new information can invalidate conclusions flies ( tweety ) ↔ bird ( tweety ) ∧ ¬ penguin ( tweety ) bird ( tweety ) ↔ ⊤ penguin ( tweety ) ↔ ⊥ | = { bird ( tweety ) , ¬ penguin ( tweety ) , flies ( tweety ) } General approach to integrate new information into reasoning process? G, Janhunen, Jost, Kaminski, Schaub ASP Solving for Expanding Universes 4 / 13

Motivation Multi-shot Solving Input Output Ground Solve Traditional ASP systems were devised for one-shot solving Modern ASP systems allow for multi-shot solving in a reactive way New properties or objects must be integrated dynamically Due to non-monotonicity, new information can invalidate conclusions flies ( X ) ← bird ( X ) , ∼ penguin ( X ) bird ( tweety ) ← penguin ( tweety ) ← | = { bird ( tweety ) , ¬ penguin ( tweety ) , flies ( tweety ) } General approach to integrate new information into reasoning process? G, Janhunen, Jost, Kaminski, Schaub ASP Solving for Expanding Universes 4 / 13

Motivation Multi-shot Solving Input Output Ground Solve Traditional ASP systems were devised for one-shot solving Modern ASP systems allow for multi-shot solving in a reactive way New properties or objects must be integrated dynamically Due to non-monotonicity, new information can invalidate conclusions flies ( X ) ← bird ( X ) , ∼ penguin ( X ) bird ( tweety ) ← penguin ( tweety ) ← | = { bird ( tweety ) , ¬ penguin ( tweety ) , flies ( tweety ) } General approach to integrate new information into reasoning process? G, Janhunen, Jost, Kaminski, Schaub ASP Solving for Expanding Universes 4 / 13

Motivation Multi-shot Solving Input Output Ground Solve Traditional ASP systems were devised for one-shot solving Modern ASP systems allow for multi-shot solving in a reactive way New properties or objects must be integrated dynamically Due to non-monotonicity, new information can invalidate conclusions flies ( tweety ) ↔ bird ( tweety ) ∧ ¬ penguin ( tweety ) bird ( tweety ) ↔ ⊤ penguin ( tweety ) ↔ ⊤ | = { bird ( tweety ) , penguin ( tweety ) , ¬ flies ( tweety ) } General approach to integrate new information into reasoning process? G, Janhunen, Jost, Kaminski, Schaub ASP Solving for Expanding Universes 4 / 13

Motivation Multi-shot Solving Input Output Ground Solve Traditional ASP systems were devised for one-shot solving Modern ASP systems allow for multi-shot solving in a reactive way New properties or objects must be integrated dynamically Due to non-monotonicity, new information can invalidate conclusions flies ( tweety ) ↔ bird ( tweety ) ∧ ¬ penguin ( tweety ) bird ( tweety ) ↔ ⊤ penguin ( tweety ) ↔ ⊤ | = { bird ( tweety ) , penguin ( tweety ) , ¬ flies ( tweety ) } General approach to integrate new information into reasoning process? G, Janhunen, Jost, Kaminski, Schaub ASP Solving for Expanding Universes 4 / 13

Motivation Basic Idea View arrival of new objects as addition of new constants ➥ Successively expanding Herbrand universe New constants induce new ground instances of rules ➥ Disjoint partition and modular composition of ground program ✘ New ground instances defining older atoms invalidate completion! Contribution ✔ Translation approach guaranteeing modularity at level of completion 1 New ground instances of rules define new expansion atoms 2 Expansion atoms are interconnected to accumulate derivations 3 Accumulated derivations are propagated to original ground atoms a a 1 a 2 a 3 a 4 a 5 r 1 1 · · · r 1 r 2 1 · · · r 2 r 3 1 · · · r 3 r 4 1 · · · r 4 n 1 n 2 n 3 n 4 G, Janhunen, Jost, Kaminski, Schaub ASP Solving for Expanding Universes 5 / 13

Motivation Basic Idea View arrival of new objects as addition of new constants ➥ Successively expanding Herbrand universe New constants induce new ground instances of rules ➥ Disjoint partition and modular composition of ground program ✘ New ground instances defining older atoms invalidate completion! Contribution ✔ Translation approach guaranteeing modularity at level of completion 1 New ground instances of rules define new expansion atoms 2 Expansion atoms are interconnected to accumulate derivations 3 Accumulated derivations are propagated to original ground atoms a a 1 a 2 a 3 a 4 a 5 r 1 1 · · · r 1 r 2 1 · · · r 2 r 3 1 · · · r 3 r 4 1 · · · r 4 n 1 n 2 n 3 n 4 G, Janhunen, Jost, Kaminski, Schaub ASP Solving for Expanding Universes 5 / 13

Motivation Basic Idea View arrival of new objects as addition of new constants ➥ Successively expanding Herbrand universe New constants induce new ground instances of rules ➥ Disjoint partition and modular composition of ground program ✘ New ground instances defining older atoms invalidate completion! Contribution ✔ Translation approach guaranteeing modularity at level of completion 1 New ground instances of rules define new expansion atoms 2 Expansion atoms are interconnected to accumulate derivations 3 Accumulated derivations are propagated to original ground atoms a a 1 a 2 a 3 a 4 a 5 r 1 1 · · · r 1 r 2 1 · · · r 2 r 3 1 · · · r 3 r 4 1 · · · r 4 n 1 n 2 n 3 n 4 G, Janhunen, Jost, Kaminski, Schaub ASP Solving for Expanding Universes 5 / 13

Motivation Basic Idea View arrival of new objects as addition of new constants ➥ Successively expanding Herbrand universe New constants induce new ground instances of rules ➥ Disjoint partition and modular composition of ground program ✘ New ground instances defining older atoms invalidate completion! Contribution ✔ Translation approach guaranteeing modularity at level of completion 1 New ground instances of rules define new expansion atoms 2 Expansion atoms are interconnected to accumulate derivations 3 Accumulated derivations are propagated to original ground atoms a a 1 a 2 a 3 a 4 a 5 r 1 1 · · · r 1 r 2 1 · · · r 2 r 3 1 · · · r 3 r 4 1 · · · r 4 n 1 n 2 n 3 n 4 G, Janhunen, Jost, Kaminski, Schaub ASP Solving for Expanding Universes 5 / 13