Scientific Thinking - 1 A. It is not what the man of science believes that distinguishes him, but how and why he believes it. B. A hypothesis is scientific only if it is testable, that is, only if it predicts something other than what it was introduced to explain. A hypothesis should state the test conditions that could render it false – falsifiability.

Scientific Thinking - 2 C. Other things being equal, the best hypothesis is the one that is the most fruitful, that is, makes the most novel predictions. D. Other things being equal, the best hypothesis is the one that has the greatest scope, that is, that explains and predicts the most diverse phenomena.

Scientific Thinking - 3 E. Other things being equal, the best hypothesis is the simplest one, that is, the one that makes the fewest assumptions. F. Other things being equal, the best hypothesis is the most conservative, that is, the one that fits best with established beliefs.

Scientific Thinking - 4 G. We should accept an extraordinary hypothesis only if no ordinary one will do. H. When two or more hypotheses compete, we should make a new observation, the result of which shall eliminate some of them.

Occam's razor – 1 The Occam's razor principle (of William of Ockham) states that the explanation of any phenomenon should make as few assumptions as possible. The Occam's razor principle (of William of Ockham) states that the explanation of any phenomenon should make as few assumptions as possible. The goal is that of eliminating, or "shaving off", the number of observable predictions of the explanatory assumptions or theory. A simpler set of assumptions has less consequences. The goal is that of eliminating, or "shaving off", the number of observable predictions of the explanatory assumptions or theory. A simpler set of assumptions has less consequences. (see Wikipedia)

Occam's razor – 2 Given two equally valid explanations for a phenomenon, one should embrace the less complicated formulation. Given two equally valid explanations for a phenomenon, one should embrace the less complicated formulation. And, when multiple competing theories have equal predictive powers, select those that introduce the fewest assumptions and the fewest hypothetical entities. And, when multiple competing theories have equal predictive powers, select those that introduce the fewest assumptions and the fewest hypothetical entities.

Abduction - 1 Abduction, or abductive reasoning, is the process of reasoning to the best explanations. Abduction, or abductive reasoning, is the process of reasoning to the best explanations. It is the reasoning process that starts from a set of observations or conclusions and derives their most likely explanations. It is the reasoning process that starts from a set of observations or conclusions and derives their most likely explanations. The term abduction is sometimes used to mean just the generation of hypotheses to explain observations or conclusions, given a theory. The term abduction is sometimes used to mean just the generation of hypotheses to explain observations or conclusions, given a theory.

Abduction - 2 Deduction and abduction differ in the direction in which a rule like " a entails b " is used for inference: Deduction and abduction differ in the direction in which a rule like " a entails b " is used for inference: Deduction allows deriving b as a consequence of a ; i.e., deduction is the process of deriving the consequences of what is known. Deduction allows deriving b as a consequence of a ; i.e., deduction is the process of deriving the consequences of what is known. Abduction allows deriving a as an hypothetical explanation of b. Abduction allows deriving a as an hypothetical explanation of b.

Abduction - 3 Abduction works in reverse to deduction, by allowing the precondition a of "a entails b " to be derived from the consequence b. I.e. abduction is the process of explaining what is known. Abduction works in reverse to deduction, by allowing the precondition a of "a entails b " to be derived from the consequence b. I.e. abduction is the process of explaining what is known. Charles Peirce introduced abduction into logic, to mean the use of a rule or hypothetical fact to explain an observation, e.g. "if it rains the grass is wet" is used to explain why the grass is wet, given that it has rained, or vice-versa. Charles Peirce introduced abduction into logic, to mean the use of a rule or hypothetical fact to explain an observation, e.g. "if it rains the grass is wet" is used to explain why the grass is wet, given that it has rained, or vice-versa.

Abduction - 4 In logic, abduction is done from a logical theory T representing a domain and a set of observations O. In logic, abduction is done from a logical theory T representing a domain and a set of observations O. Abduction is the process of deriving a set of explanations of O according to T. For E to be an explanation of O according to T, it should satisfy two conditions: Abduction is the process of deriving a set of explanations of O according to T. For E to be an explanation of O according to T, it should satisfy two conditions: –O follows from E and T; –E is consistent with T.

Abduction - 5 In formal logic, O and E are assumed to be sets of literals. The two conditions for E being an explanation of O according to theory T are: In formal logic, O and E are assumed to be sets of literals. The two conditions for E being an explanation of O according to theory T are: – T ⋃ E ⊨ O ; – T ⋃ E is consistent. Among the possible explanations E satisfying these two conditions, a condition of minimality is usually imposed to avoid irrelevant facts (i.e. not contributing to the entailment of O ) to be included in the explanations. Among the possible explanations E satisfying these two conditions, a condition of minimality is usually imposed to avoid irrelevant facts (i.e. not contributing to the entailment of O ) to be included in the explanations.

Abduction - 6 An application of abduction is that of detecting faults in systems: given a theory relating faults with their effects and a set of observed effects, abduction can be used to derive sets of faults that are likely to be the cause of the problem. An application of abduction is that of detecting faults in systems: given a theory relating faults with their effects and a set of observed effects, abduction can be used to derive sets of faults that are likely to be the cause of the problem. Belief revision, the process of adapting beliefs in view of new information, is another field in which abduction has been applied. The main problem of belief revision is that the new information may be inconsistent with the corpus of beliefs, while the result of the incorporation must not be inconsistent. Belief revision, the process of adapting beliefs in view of new information, is another field in which abduction has been applied. The main problem of belief revision is that the new information may be inconsistent with the corpus of beliefs, while the result of the incorporation must not be inconsistent.

Models -1 Scientists often describe what they do as constructing models. Understanding scientific reasoning requires understanding something about models and how they are used in science. Scientists often describe what they do as constructing models. Understanding scientific reasoning requires understanding something about models and how they are used in science. There are at least 3 kinds of models: There are at least 3 kinds of models: –scale: e.g. model airplane –analog: e.g. conventional city maps –theoretical: e.g. Newtonian physics equations

Models -2 Models need to be put in correspondence with reality, through hypotheses and interpretations. Models need to be put in correspondence with reality, through hypotheses and interpretations. A model may predict something that is not confirmed, in which case the model is incorrect. A model may predict something that is not confirmed, in which case the model is incorrect. A model may fail to predict something it should be able to, in which case it is incomplete. A model may fail to predict something it should be able to, in which case it is incomplete. Like other mal-functioning artefacts, mistaken models can be diagnosed. Like other mal-functioning artefacts, mistaken models can be diagnosed.

Model-based diagnosis - 1 Diagnosis is concerned with the development of algorithms and techniques that can determine whether the behaviour of a system (or artefact) is correct. The artefact may be a theory. Diagnosis is concerned with the development of algorithms and techniques that can determine whether the behaviour of a system (or artefact) is correct. The artefact may be a theory. If the system is not functioning correctly, the algorithm should be able to determine, as accurately as possible, which part of the system is failing, and the kind of fault it is facing. If the system is not functioning correctly, the algorithm should be able to determine, as accurately as possible, which part of the system is failing, and the kind of fault it is facing. The computation is based on observations which provide information on the current behaviour. The computation is based on observations which provide information on the current behaviour.

Model-based diagnosis - 2 Model-based diagnosis is an example of abductive reasoning using a model of the system: Model-based diagnosis is an example of abductive reasoning using a model of the system:

Model-based diagnosis - 3 A model describes the behaviour of the system, or artefact. The model can itself be the artefact. A model describes the behaviour of the system, or artefact. The model can itself be the artefact. It an abstraction of the behaviour of the system and can be incomplete. The faulty behaviour may be little-known, and the fault model might not be represented. If the model is a program: debugging. It an abstraction of the behaviour of the system and can be incomplete. The faulty behaviour may be little-known, and the fault model might not be represented. If the model is a program: debugging. Given the observations, the diagnoser simulates the system using the model, and compares the observations actually made to the observations predicted by the simulation. Given the observations, the diagnoser simulates the system using the model, and compares the observations actually made to the observations predicted by the simulation.

Model-based diagnosis - 4 The modelling can be expressed by the rules (where Ab is the Abnormality predicate) : The modelling can be expressed by the rules (where Ab is the Abnormality predicate) : If the behaviour of the system is not abnormal (i.e. normal), then the internal (unobservable) behaviour will be Int1 and the observable one Obs1. If the behaviour of the system is not abnormal (i.e. normal), then the internal (unobservable) behaviour will be Int1 and the observable one Obs1. Otherwise, the internal behaviour will be Int2 and the observable behaviour Obs2. Otherwise, the internal behaviour will be Int2 and the observable behaviour Obs2. Given the observations Obs, the problem is to determine whether the system behaviour is normal or not ( ¬ Ab(S) or Ab(S) ). This is an example of abductive reasoning. Given the observations Obs, the problem is to determine whether the system behaviour is normal or not ( ¬ Ab(S) or Ab(S) ). This is an example of abductive reasoning.