Defeasible reasoning

Though Aristotle differentiated the forms of reasoning that are valid for logic and philosophy from the more general ones that are used in everyday life (see dialectics and rhetoric), subsequent philosophers mainly concentrated on deductive reasoning. It wasn't until logical positivism started falling out of favour that philosophers like Roderick Chisholm and John L. Pollock renewed an interest in defeasible reasoning. ...

See also:

Defeasible reasoning, Defeasible reasoning - Origins in philosophy, Defeasible reasoning - Artificial intelligence

Read more here: » Defeasible reasoning: Encyclopedia II - Defeasible reasoning - Origins in philosophy

Abduction, or abductive reasoning, is the process of reasoning to the best explanations. In other words, it is the reasoning process that starts from a set of facts and derives their most likely explanations. The term abduction is sometimes used to mean just the generation of hypotheses to explain observations or conclusions, but the former definition is more common both in philosophy and computing. Deduction and abduction differ in the direction in which a rule like “a entail ...

Including:

• Abductive reasoning - Logic-based Abduction
• Abductive reasoning - Set-Cover Abduction
• Abductive reasoning - History of the concept
• Abductive reasoning - Applications

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Falsifiability is an important concept in the philosophy of science that amounts to the apparently paradoxical idea that a proposition or theory cannot be scientific if it does not admit the possibility of being shown false. Falsifiable does not mean false. For a proposition to be falsifiable, it must be at least in principle possible to make an observation that would show the proposition to be false, even if that observation had not been made. For example, the proposition "All crows are black" would be falsified ...

Including:

• Falsifiability - Naïve falsification
• Falsifiability - Falsificationism
• Falsifiability - Popper's swan argument
• Falsifiability - Formal logical arguments
• Falsifiability - The criterion of demarcation
• Falsifiability - Criticism
• Falsifiability - From scientists
• Falsifiability - Some examples
• Falsifiability - Mathematics
• Falsifiability - Ethics
• Falsifiability - Theism
• Falsifiability - Conspiracy theories
• Falsifiability - Economics
• Falsifiability - Historicism
• Falsifiability - Solipsism
• Falsifiability - Physical laws

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In deductive reasoning, given true premises, the conclusion must follow and it cannot be false. This type of reasoning is non-ampliative - it does not increase one's knowledge base - since the conclusion is inherent to the premises. A classical example of deductive reasoning are syllogisms for example: all humans are mortal, Socrates is a man, therefore, Socrates is mortal. In inductive reasoning, on the other hand, when the premises are true, then the conclusion follows with some degree of probab ...

See also:

Reasoning, Reasoning - Types of reasoning

Read more here: » Reasoning: Encyclopedia II - Reasoning - Types of reasoning

In the following, how the frame problem is solved in various formalisms is shown. The formalisms themselves are not presented in full: what is presented are simplified versions that are however sufficient to show how the frame problem is solved. Frame problem - The fluent occlusion solution. This solution was proposed by Erik Sandewall, who also defined a formal language for the specification of dynamical domains; therefore, such a domain can be first expressed in this language and then automatically translated into logic. In this article, only the expression in logic is ...

See also:

Frame problem, Frame problem - The frame problem in artificial intelligence, Frame problem - Solutions to the frame problem, Frame problem - The fluent occlusion solution, Frame problem - The predicate completion solution, Frame problem - The successor state axioms solution, Frame problem - The fluent calculus solution, Frame problem - The event calculus solution, Frame problem - Action description languages, Frame problem - Related problems, Frame problem - The frame problem in philosophy

Read more here: » Frame problem: Encyclopedia II - Frame problem - Solutions to the frame problem

The original definition of circumscription proposed by McCarthy is about first-order logic. The role of variables in propositional logic (something that can be true or false) is played in first-order logic by predicates. Namely, a propositional formula can be expressed in first-order logic by replacing each propositional variable with a predicate of zero arity (i.e., a predicate with no arguments). Therefore, minimization is done on predicates in the first-order logic version of circumscription: the circumscription of a formula ...

See also:

Circumscription, Circumscription - The propositional case, Circumscription - Fixed and varying predicates, Circumscription - Predicate circumscription, Circumscription - Pointwise circumscription, Circumscription - Domain and Formula Circumscription, Circumscription - Theory curbing

Read more here: » Circumscription: Encyclopedia II - Circumscription - Predicate circumscription

Claims about verifiability and falsifiability have been used to criticize various controversial views. Examining these examples shows the usefulness of falsifiability by showing us where to look when attempting to criticise a theory. Non-falsifiable theories can usually be reduced to a simple uncircumscribed existential statement, such as there exists a green swan. It is entirely possible to verify that the theory is true, simply by producing the green swan. But since this statement does not specify when or where the green swan exists, it is simply not possible to show that the swan does not exist, and so i ...

See also:

Falsifiability, Falsifiability - Naïve falsification, Falsifiability - Falsificationism, Falsifiability - Popper's swan argument, Falsifiability - Formal logical arguments, Falsifiability - The criterion of demarcation, Falsifiability - Criticism, Falsifiability - From scientists, Falsifiability - Some examples, Falsifiability - Mathematics, Falsifiability - Ethics, Falsifiability - Theism, Falsifiability - Conspiracy theories, Falsifiability - Economics, Falsifiability - Historicism, Falsifiability - Solipsism, Falsifiability - Physical laws

Read more here: » Falsifiability: Encyclopedia II - Falsifiability - Some examples

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: See also:

Abductive reasoning, Abductive reasoning - Logic-based Abduction, Abductive reasoning - Set-Cover Abduction, Abductive reasoning - History of the concept, Abductive reasoning - Applications

Read more here: » Abductive reasoning: Encyclopedia II - Abductive reasoning - Logic-based Abduction

Pointwise circumscription is a variant of first-order circumscription that has been introduced by Vladimir Lifschitz. In the propositional case, pointwise and predicate circumscription coincide. The rationale of pointwise circumscription it minimize the value of a predicate for each tuple of values separately, rather than minimizing the extension of the predicate. For example, there are two models of with domain {a,b}, one setting P(a) = P(b) = f ...

See also:

Circumscription, Circumscription - The propositional case, Circumscription - Fixed and varying predicates, Circumscription - Predicate circumscription, Circumscription - Pointwise circumscription, Circumscription - Domain and Formula Circumscription, Circumscription - Theory curbing

Read more here: » Circumscription: Encyclopedia II - Circumscription - Pointwise circumscription

The philosopher Charles Peirce introduced abduction into modern logic. In his works before 1900, he mostly uses the term to mean the use of a known rule to explain an observation, e.g., “if it rains the grass is wet” is a known rule used to explain that the grass is wet. He later used the term to mean creating new rules to explain new observations, emphasising that abduction is the only logical process that actually creates anything new. Namely, he described the process of science as a combination of abduction, deduction and implicati ...

See also:

Abductive reasoning, Abductive reasoning - Logic-based Abduction, Abductive reasoning - Set-Cover Abduction, Abductive reasoning - History of the concept, Abductive reasoning - Applications

Read more here: » Abductive reasoning: Encyclopedia II - Abductive reasoning - History of the concept

An earlier formulation of circumscription by McCarthy is based on minimizing the domain of first-order models, rather than the extension of predicates. Namely, a model is considered less than another if it has a smaller domain, and the two models coincide on the evaluation of the common tuples of values. This version of circumscription can be reduced to predicate circumscription. Formula circumscription was a later formalism introduced by McCarthy. This is a generalization of circumscription in which the extension of a formula is mini ...

See also:

Circumscription, Circumscription - The propositional case, Circumscription - Fixed and varying predicates, Circumscription - Predicate circumscription, Circumscription - Pointwise circumscription, Circumscription - Domain and Formula Circumscription, Circumscription - Theory curbing

Read more here: » Circumscription: Encyclopedia II - Circumscription - Domain and Formula Circumscription

The frame problem occurs even in very simple domains. A scenario with a door, which can be open or closed, and a light, which can be on or off, is statically represented by two propositions open and on. If these conditions can change, they are better represented by two predicates open(t) and on(t) that depend on time; such predicates are called fluents. A domain in which the door is closed, the light is off, and the door is opened at time 0, can be directly represente ...

See also:

Frame problem, Frame problem - The frame problem in artificial intelligence, Frame problem - Solutions to the frame problem, Frame problem - The fluent occlusion solution, Frame problem - The predicate completion solution, Frame problem - The successor state axioms solution, Frame problem - The fluent calculus solution, Frame problem - The event calculus solution, Frame problem - Action description languages, Frame problem - Related problems, Frame problem - The frame problem in philosophy

Read more here: » Frame problem: Encyclopedia II - Frame problem - The frame problem in artificial intelligence

A different formalization of abduction is based on inverting the function that calculates the visible effects of the hypotheses. Formally, we are given a set of hypotheses H and a set of manifestations M; they are related by the domain knowledge, represented by a function e that takes as an argument a set of hypotheses and gives as a result the corresponding set of manifestations. In other words, for every subset of the hypotheses , their effects are kn ...

See also:

Abductive reasoning, Abductive reasoning - Logic-based Abduction, Abductive reasoning - Set-Cover Abduction, Abductive reasoning - History of the concept, Abductive reasoning - Applications

Read more here: » Abductive reasoning: Encyclopedia II - Abductive reasoning - Set-Cover Abduction

The extension of circumscription with fixed and varying predicates is due to Vladimir Lifschitz. The idea is that some conditions are not to be minimized. In propositional logic terms, some variables are not to be falsified if possible. In particular, two kind of variables can be considered: varying  these are variables that are not to be taken into account at all in the course of minimization; fixed  these are variables considered fixed while doing a minimization; in other words, minimization can be done only by ...

See also:

Circumscription, Circumscription - The propositional case, Circumscription - Fixed and varying predicates, Circumscription - Predicate circumscription, Circumscription - Pointwise circumscription, Circumscription - Domain and Formula Circumscription, Circumscription - Theory curbing

Read more here: » Circumscription: Encyclopedia II - Circumscription - Fixed and varying predicates

Circumscription does not always correctly handle disjunctive information. Ray Reiter provided the following example: a coin is tossed over a checkboard, and the result is that the coin is either on a black area, or on a white area, or both. However, there are a large number of other possible places where the coin is not supposed to be on; for example, it is implicit that the coin is not on the floor, or on the refrigerator, or on the moon surface. Circumscription can therefore be used to minimize the extension of OSee also:

Circumscription, Circumscription - The propositional case, Circumscription - Fixed and varying predicates, Circumscription - Predicate circumscription, Circumscription - Pointwise circumscription, Circumscription - Domain and Formula Circumscription, Circumscription - Theory curbing

Read more here: » Circumscription: Encyclopedia II - Circumscription - Theory curbing

While circumscription was initially defined in the first-order logic case, the particularization to the propositional case is easier to define. Given a propositional formula T, its circumscription is the formula having only the models of T with a minimal amount of variables assigned to true. Formally, propositional models can be represented by set of propositional variables; namely, each model is represented by the set of propositional variables it assign to true. ...

See also:

Circumscription, Circumscription - The propositional case, Circumscription - Fixed and varying predicates, Circumscription - Predicate circumscription, Circumscription - Pointwise circumscription, Circumscription - Domain and Formula Circumscription, Circumscription - Theory curbing

Read more here: » Circumscription: Encyclopedia II - Circumscription - The propositional case

Thomas Kuhn’s influential book The Structure of Scientific Revolutions argued that scientists work within a conceptual paradigm that determines the way in which they view the world. Scientists will go to great length to defend their paradigm against falsification, by the addition of ad hoc hypotheses to existing theories. Changing one's 'paradigm' is not easy, and only through some pain and angst does science (at the level of ...

See also:

Falsifiability, Falsifiability - Naïve falsification, Falsifiability - Falsificationism, Falsifiability - Popper's swan argument, Falsifiability - Formal logical arguments, Falsifiability - The criterion of demarcation, Falsifiability - Criticism, Falsifiability - From scientists, Falsifiability - Some examples, Falsifiability - Mathematics, Falsifiability - Ethics, Falsifiability - Theism, Falsifiability - Conspiracy theories, Falsifiability - Economics, Falsifiability - Historicism, Falsifiability - Solipsism, Falsifiability - Physical laws

Read more here: » Falsifiability: Encyclopedia II - Falsifiability - Criticism

Popper proposed falsification as a way of determining if a theory is scientific or not. If a theory is falsifiable, then it is scientific; if it is not falsifiable, then it is not science. Popper uses this criterion of demarcation to draw a sharp line between scientific and unscientific theories. Some have taken this principle to an extreme to cast doubt on the scientific validity of many disciplines (such as macroevolution and Cosmology). Falsifiability was one of the criteria used by Judge William Overton to determine that 'creation science' was not ...

See also:

Falsifiability, Falsifiability - Naïve falsification, Falsifiability - Falsificationism, Falsifiability - Popper's swan argument, Falsifiability - Formal logical arguments, Falsifiability - The criterion of demarcation, Falsifiability - Criticism, Falsifiability - From scientists, Falsifiability - Some examples, Falsifiability - Mathematics, Falsifiability - Ethics, Falsifiability - Theism, Falsifiability - Conspiracy theories, Falsifiability - Economics, Falsifiability - Historicism, Falsifiability - Solipsism, Falsifiability - Physical laws

Read more here: » Falsifiability: Encyclopedia II - Falsifiability - The criterion of demarcation

The falsification of theories occurs through modus tollens, via some observation. Suppose some theory T implies an observation O: The required observation, however, is not made, therefore So by Modus Tollens, ...

See also:

Falsifiability, Falsifiability - Naïve falsification, Falsifiability - Falsificationism, Falsifiability - Popper's swan argument, Falsifiability - Formal logical arguments, Falsifiability - The criterion of demarcation, Falsifiability - Criticism, Falsifiability - From scientists, Falsifiability - Some examples, Falsifiability - Mathematics, Falsifiability - Ethics, Falsifiability - Theism, Falsifiability - Conspiracy theories, Falsifiability - Economics, Falsifiability - Historicism, Falsifiability - Solipsism, Falsifiability - Physical laws

Read more here: » Falsifiability: Encyclopedia II - Falsifiability - Formal logical arguments

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 which can account for the phenomena which falsified the prior theory, that is, with greater explanatory power. Thus, Aristotelian mechanics explained observations of objects in everyday situations, but was falsified by Galileo’s experiments, and was itself replaced by Newtonian mechanics which accounted for the phenomena noted by Galile ...

See also:

Falsifiability, Falsifiability - Naïve falsification, Falsifiability - Falsificationism, Falsifiability - Popper's swan argument, Falsifiability - Formal logical arguments, Falsifiability - The criterion of demarcation, Falsifiability - Criticism, Falsifiability - From scientists, Falsifiability - Some examples, Falsifiability - Mathematics, Falsifiability - Ethics, Falsifiability - Theism, Falsifiability - Conspiracy theories, Falsifiability - Economics, Falsifiability - Historicism, Falsifiability - Solipsism, Falsifiability - Physical laws

Read more here: » Falsifiability: Encyclopedia II - Falsifiability - Falsificationism