Layer Supported Models of Logic PRograms

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Layer Supported Models of Logic PRograms

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Sep 10, 2009 - mountain â not travel travel â not beach, passport ok passport ok â not expired passport expired passport â not passport ok. L. S. models:.

Layer Supported Models of Logic PRograms Luís Moniz Pereira, Alexandre Miguel Pinto CENTRIA - Universidade Nova de Lisboa

LPNMR’09, Potsdam, 15 September

Thursday, September 10, 2009

Outline Layering of Logic Programs Layer Supported Models Properties Conclusions

Thursday, September 10, 2009

Layering of Logic Programs Layer 2 Odd Loop

beach mountain travel

← ← ←

not mountain not travel not beach, passport ok

Layer 1 Even Loop

passport ok expired passport

← ←

not expired passport not passport ok

Layering puts Rules in Layers, not Atoms All rules of a loop are in the same layer Non-loop dependencies are mapped into different layers (Cf. rules for travel and passport_ok) Thursday, September 10, 2009

Layer Supported Models L. S. models:

beach mountain travel

← ← ←

not mountain not travel not beach, passport ok

{p_ok, b, m}, {p_ok, m, t}, {p_ok, t, b}, {e_p, m}

passport ok expired passport

← ←

not expired passport not passport ok

L. S. models: {p_ok}, {e_p}

Global models are combinations of individual layers’ minimal models, but... ...only of those minimal models that respect the WFM of all rules of the layers below This program has no Stable Models Thursday, September 10, 2009

Properties Conservative Extension of Stable Models Guarantee of Model Existence Relevance (strict call-graph top-down querying is sound) --- no need to compute whole models

Cumulativity L.S. Models are the minimal models that respect the Well-Founded Model Thursday, September 10, 2009

Conclusions LSM semantics builds upon our LM semantics in PADL’09 LSM introduces a new refined notion of layering which captures more structural information So that LSM respects the Well-Founded Model Current work: implementation of efficient meta-interpreter for top-down querying Thursday, September 10, 2009

Thank You!

Thursday, September 10, 2009