Logic Program Revision The problem: The problem: –A LP represents consistent incomplete knowledge; –New factual information comes. –How to incorporate the new information? The solution: The solution: –Add the new facts to the program; –If the union is consistent this is the result; –Otherwise restore consistency to the union. The new problem: The new problem: –How to restore consistency to an inconsistent program?

Simple revision example - 1 P:flies(X)  bird(X), not ab(X). bird(a) . ab(X)  penguin(X). Sois true. Next, we learn. is consistent,is false, is. Nothing needs to be done. So flies(a) is true. Next, we learn penguin(a). P  {penguin(a)} is consistent, flies(a) is false, not ab(a) is defeated. Nothing needs to be done. We learn instead.is We learn instead ¬flies(a). flies(a) is rebutted. is inconsistent. What to do? P  {¬flies(a)} is inconsistent. What to do? Since the inconsistency rests on the assumption, revise that assumption, e.g. by adding the fact, thereby obtaining a new program. Since the inconsistency rests on the assumption not ab(a), revise that assumption, e.g. by adding the fact ab(a), thereby obtaining a new program P’.

Simple revision example - 2 P:flies(X)  bird(X), not ab(X). bird(a) . ab(X)  penguin(X). If an assumption supports contradiction, then go back on that assumption: the Reductio ad absurdum principle. Later we learnis inconsistent. Later we learn flies(a). P’  {flies(a)} is inconsistent. The contradiction does not depend on assumptions. Cannot remove contradiction! Some programs are non-revisable:

Which assumptions remove? normalWheel  not flatTyre, not brokenSpokes. flatTyre  leakyValve. ¬ normalWheel  wobblyWheel. flatTyre  puncturedTube. wobblyWheel . Contradiction can be removed by either revising or ( or both). Contradiction can be removed by either revising not flatTyre or not brokenSpokes ( or both). We’d like to delve deeper into the model and, instead of, revise either We’d like to delve deeper into the model and, instead of not flatTyre, revise either or ( or both). not leakyValve or not puncturedTube ( or both).

Revisables not {leakyValve, punctureTube, brokenSpokes} Revisions in this case are:,, and {not lv}, {not pt}, and {not bs} Solution: define a set of Solution: define a set of revisables normalWheel  not flatTyre, not brokenSpokes. flatTyre  leakyValve. ¬ normalWheel  wobblyWheel. flatTyre  puncturedTube. wobblyWheel .

Integrity Constraints For convenience, instead of: For convenience, instead of: ¬ normalWheel  wobblyWheel we may use the denial:   normalWheel, wobblyWheel

Example - 1 Rev = Rev = not {a,b,c}   p, q p  not a. q  not b, r. r  not b. r  not c.  pq not arnot b not c Support sets are: {not a, not b} and. and {not a, not b, not c}. Removal sets are:and. Removal sets are: {not a} and {not b}.

Example - 2 In 2-valued revision: –some removals must be deleted; –the process must be iterated.   p.   a.   b, not c. p  not a, not b.  a X p not a not b b not c X The only support is. The only support is {not a, not b}. Removals areand. Removals are {not a} and {not b}. is contradictory (and unrevisable). P U {a} is contradictory (and unrevisable). is contradictory (though revisable). P U {b} is contradictory (though revisable).But:

Revision and Diagnosis In model based diagnosis one has: In model based diagnosis one has: –A programwith the model of a system, with the correct and, possibly, the incorrect behaviours. –A program P with the model of a system, with the correct and, possibly, the incorrect behaviours. –A set of observationsinconsistent with, or not explained by. –A set of observations O inconsistent with P, or not explained by P. The diagnoses of the system are the revisions of The diagnoses of the system are the revisions of P U O

Falsifiability - 6 Naïve falsification considers scientific statements individually. But scientific theories are formed from groups of these sorts of statements, and it is these groups that must be accepted or rejected by scientists. Scientific theories can always be defended by the addition of ad hoc hypotheses. Naïve falsification considers scientific statements individually. But scientific theories are formed from groups of these sorts of statements, and it is these groups that must be accepted or rejected by scientists. Scientific theories can always be defended by the addition of ad hoc hypotheses. As Popper put it, a is required on the part of the scientist to accept or reject the statements that go to make up a theory or that might falsify it. As Popper put it, a decision is required on the part of the scientist to accept or reject the statements that go to make up a theory or that might falsify it.

Falsifiability - 7 At some point, the weight of the ad hoc hypotheses and disregarded falsifying observations will become so great that it becomes unreasonable to support the base theory any longer, and a decision will be made to reject it. At some point, the weight of the ad hoc hypotheses and disregarded falsifying observations will become so great that it becomes unreasonable to support the base theory any longer, and a decision will be made to reject it. In place of naïve falsification, Popper envisioned science as evolving by the successive rejection of falsified theories, rather than falsified statements. In place of naïve falsification, Popper envisioned science as evolving by the successive rejection of falsified theories, rather than falsified statements. Falsified theories are to be replaced by theories that account for the phenomena which falsified the prior theory, i.e. with greater explanatory power. Falsified theories are to be replaced by theories that account for the phenomena which falsified the prior theory, i.e. with greater explanatory power.

Falsifiability - 8 Popper proposed falsification as a way to determine if a theory is scientific. If a theory is falsifiable, then it is scientific; if it is not, then it is not science. A theory not open to falsification requires faith that it is not false. He uses this criterion of demarcation to draw a sharp line between scientific and unscientific theories. Popper proposed falsification as a way to determine if a theory is scientific. If a theory is falsifiable, then it is scientific; if it is not, then it is not science. A theory not open to falsification requires faith that it is not false. He uses this criterion of demarcation to draw a sharp line between scientific and unscientific theories. Falsifiability was one of the criteria used by Judge Overton to determine that 'creation science' was not scientific and should not be taught in public schools. It was enshrined in United States law for whether scientific evidence is admissible in a jury trial. Falsifiability was one of the criteria used by Judge Overton to determine that 'creation science' was not scientific and should not be taught in public schools. It was enshrined in United States law for whether scientific evidence is admissible in a jury trial.

Scientific method - 1 Scientific method is a body of techniques for investigating phenomena and acquiring new knowledge, as well as for correcting and integrating previous knowledge. It is based on observable, empirical, measurable evidence, and subject to laws of reasoning. Scientific method is a body of techniques for investigating phenomena and acquiring new knowledge, as well as for correcting and integrating previous knowledge. It is based on observable, empirical, measurable evidence, and subject to laws of reasoning. Although specialized procedures vary from one field of inquiry to another, there are identifiable features that distinguish scientific inquiry from other methods of developing knowledge. Although specialized procedures vary from one field of inquiry to another, there are identifiable features that distinguish scientific inquiry from other methods of developing knowledge.