Download presentation

Presentation is loading. Please wait.

Published byDominik Maulding Modified over 2 years ago

1
The coherence principle Generalizing WFS in the same way yields unintuitive results: pacifist(X) not hawk(X) hawk(X) not pacifist(X) ¬ pacifist(a) –Using the same method the WFS is: {¬pacifist(a)} –Though it is explicitly stated that a is non-pacifist, not pacifist(a) is not assumed, and so hawk(a) cannot be concluded. Coherence is not satisfied... Ü Coherence must be imposed

2
Imposing Coherence Coherence is: ¬L T L F, for objective L According to the WFS definition, everything is false that doesn’t belong to (T) To impose coherence, when applying (T) simply delete all rules for the objective complement of literals in T “If L is explicitly true then when computing undefined literals forget all rules with head ¬L”

3
WFSX definition D The semi-normal version of P, P s, is obtained by adding not ¬L to every rule of P with head L D An interpretation (T U not F) is a PSM of ELP P iff: T = P Ps (T) T Ps (T) F = H P - Ps (T) T The WFSX semantics is determined by the knowledge ordering least PSM (wrt )

4
WFSX example P:pacifist(X) not hawk(X) hawk(X) not pacifist(X) ¬ pacifist(a) Ps:pacifist(X) not hawk(X), not ¬pacifist(X) hawk(X) not pacifist(X ), not ¬hawk(X) ¬pacifist(a) not pacifist(a) T 0 = {} s (T 0 ) = {¬p(a),p(a),h(a),p(b),h(b)} T 1 = {¬p(a)} s (T 1 ) = {¬p(a),h(a),p(b),h(b)} T 2 = {¬p(a),h(a)} T 3 = T 2 The WFM is: {¬p(a),h(a), not p(a), not ¬h(a), not ¬p(b), not ¬h(b)}

5
Properties of WFSX Complies with the coherence principle Coincides with WFS in normal programs If WFSX is total it coincides with the only answer-set It is sound wrt answer-sets It is supported, cumulative, and relevant Its computation is polynomial It has sound implementations (cf. below)

6
Inconsistent programs Some ELPs have no WFM. E.g. { a ¬a } What to do in these cases? Explosive approach: everything follows from contradiction taken by answer-sets gives no information in the presence of contradiction Belief revision approach: remove contradiction by revising P computationally expensive Paraconsistent approach: isolate contradiction efficient allows to reason about the non-contradictory part

7
WFSXp definition The paraconsistent version of WFSx is obtained by dropping the requirement that T and F are disjoint, i.e. dropping T Ps (T) D An interpretation, T U not F, is a PSMp P iff: T = P Ps (T) F = H P - Ps (T) T The WFSXp semantics is determined by the knowledge ordering least PSM (wrt )

8
WFSXp example P:c not ba b a ¬ a d not e Ps:c not b, not ¬c a not ¬a b a, not ¬b ¬a not a d not e, not ¬d T 0 = {} s (T 0 ) = {¬a,a,b,c,d} T 1 = {¬a,a,b,d} s (T 1 ) = {d} T 2 = {¬a,a,b,c,d} T 3 = T 2 The WFM is: {¬a,a,b,c,d, not a, not ¬a, not b, not ¬b not c, not ¬c, not ¬d, not e}

9
Surgery situation A patient arrives with: sudden epigastric pain; abdominal tenderness; signs of peritoneal irritation The rules for diagnosing are: –if he has sudden epigastric pain abdominal tenderness, and signs of peritoneal irritation, then he has perforation of a peptic ulcer or an acute pancreatitis –the former requires surgery, the latter therapeutic treatment –if he has high amylase levels, then a perforation of a peptic ulcer can be exonerated –if he has Jobert’s manifestation, then pancreatitis can be exonerated –In both situations, the pacient should not be nourished, but should take H 2 antagonists

10
LP representation perforation pain, abd-tender, per-irrit, not high-amylase pancreat pain, abd-tender, per-irrit, not jobert ¬nourish perforationh2-ant perforation ¬nourish pancreat h2-ant pancreat surgery perforationanesthesia surgery ¬surgery pancreat pain. per-irrit. ¬high-amylase. abd-tender. ¬jobert. The WFM is: {pain, abd-tender, per-irrit, ¬high-am, ¬jobert, not ¬pain, not ¬abd-tender, not ¬per-irrit, not high-am, not jobert, ¬nourish, h2-ant, not nourish, not ¬h2-ant, surgery, ¬surgery, not surgery, not ¬surgery, anesthesia, not anesthesia, not ¬anesthesia }

11
Results interpretation The symptoms are derived and non-contradictory Both perforation and pancreatitis are concluded He should not be fed ( ¬nourish ), but take H 2 antagonists The information about surgery is contradictory Anesthesia though not explicitly contradictory ( ¬anesthesia doesn’t belong to WFM) relies on contradiction (both anesthesia and not anesthesia belong to WFM) The WFM is: {pain, abd-tender, per-irrit, ¬high-am, ¬jobert, …, ¬nourish, h2-ant, not nourish, not ¬h2-ant, surgery, ¬surgery, not surgery, not ¬surgery,anesthesia, not anesthesia, not ¬anesthesia }

Similar presentations

OK

Discrete Mathematics Lecture 4 Harper Langston New York University.

Discrete Mathematics Lecture 4 Harper Langston New York University.

© 2017 SlidePlayer.com Inc.

All rights reserved.

Ads by Google

Ppt on permanent magnet dc motor Ppt on general motors india Ppt on history of badminton rules Ppt on 108 ambulance how it works Ppt on steam turbine manufacturing download Ppt on sustainable development Stem and leaf display ppt online Ppt on solar energy technology Ppt on effect of global warming on weather for 2nd Ppt on iso 9000 and 14000