Inductive reasoning

Deductive reasoning Deductive reasoning links premises with conclusions. If all premises are true, the terms are clear, and the rules of deductive logic are followed, then the conclusion reached is necessarily true. Deductive reasoning (top-down logic) contrasts with inductive reasoning (bottom-up logic) in the following way: In deductive reasoning, a conclusion is reached reductively by applying general rules that hold over the entirety of a closed domain of discourse, narrowing the range under consideration until only the conclusion(s) is left. In inductive reasoning, the conclusion is reached by generalizing or extrapolating from, i.e., there is epistemic uncertainty. Note, however, that the inductive reasoning mentioned here is not the same as induction used in mathematical proofs – mathematical induction is actually a form of deductive reasoning. Simple example[edit] An example of a deductive argument: All men are mortal.Socrates is a man.Therefore, Socrates is mortal. Law of detachment[edit] P → Q.

Logical reasoning Informally, two kinds of logical reasoning can be distinguished in addition to formal deduction: induction and abduction. Given a precondition or premise, a conclusion or logical consequence and a rule or material conditional that implies the conclusion given the precondition, one can explain that: Deductive reasoning determines whether the truth of a conclusion can be determined for that rule, based solely on the truth of the premises. Example: "When it rains, things outside get wet. The grass is outside, therefore: when it rains, the grass gets wet." Mathematical logic and philosophical logic are commonly associated with this style of reasoning.Inductive reasoning attempts to support a determination of the rule. See also[edit] References[edit] T.

Abductive reasoning Inference seeking the simplest and most likely explanation Abductive reasoning (also called abduction,[1] abductive inference,[1] or retroduction[2]) is a form of logical inference that seeks the simplest and most likely conclusion from a set of observations. It was formulated and advanced by American philosopher and logician Charles Sanders Peirce beginning in the latter half of the 19th century. Abductive reasoning, unlike deductive reasoning, yields a plausible conclusion but does not definitively verify it. Abductive conclusions do not eliminate uncertainty or doubt, which is expressed in retreat terms such as "best available" or "most likely". In the 1990s, as computing power grew, the fields of law,[3] computer science, and artificial intelligence research[4] spurred renewed interest in the subject of abduction.[5] Diagnostic expert systems frequently employ abduction.[6] Deduction, induction, and abduction [edit] Deductive reasoning allows deriving from only where . , where . . . entails

Abductive reasoning Abductive reasoning (also called abduction,[1] abductive inference[2] or retroduction[3]) is a form of logical inference that goes from an observation to a hypothesis that accounts for the observation, ideally seeking to find the simplest and most likely explanation. In abductive reasoning, unlike in deductive reasoning, the premises do not guarantee the conclusion. One can understand abductive reasoning as "inference to the best explanation".[4] The fields of law,[5] computer science, and artificial intelligence research[6] renewed interest in the subject of abduction. Diagnostic expert systems frequently employ abduction. History[edit] The American philosopher Charles Sanders Peirce (1839–1914) first introduced the term as "guessing".[7] Peirce said that to abduce a hypothetical explanation from an observed circumstance is to surmise that may be true because then would be a matter of course.[8] Thus, to abduce from involves determining that is sufficient, but not necessary, for allows deriving

Defeasible reasoning Defeasible reasoning is a kind of reasoning that is based on reasons that are defeasible, as opposed to the indefeasible reasons of deductive logic. Defeasible reasoning is a particular kind of non-demonstrative reasoning, where the reasoning does not produce a full, complete, or final demonstration of a claim, i.e., where fallibility and corrigibility of a conclusion are acknowledged. In other words defeasible reasoning produces a contingent statement or claim. Other kinds of non-demonstrative reasoning are probabilistic reasoning, inductive reasoning, statistical reasoning, abductive reasoning, and paraconsistent reasoning. Defeasible reasoning is also a kind of ampliative reasoning because its conclusions reach beyond the pure meanings of the premises. The differences between these kinds of reasoning correspond to differences about the conditional that each kind of reasoning uses, and on what premise (or on what authority) the conditional is adopted: History[edit] Specificity[edit]

Proof assistant From Wikipedia, the free encyclopedia Software tool to assist with the development of formal proofs by human–machine collaboration In computer science and mathematical logic, a proof assistant or interactive theorem prover is a software tool to assist with the development of formal proofs by human–machine collaboration. This involves some sort of interactive proof editor, or other interface, with which a human can guide the search for proofs, the details of which are stored in, and some steps provided by, a computer. A recent effort within this field is making these tools use artificial intelligence to automate the formalization of ordinary mathematics.[1] A popular front-end for proof assistants is the Emacs-based Proof General, developed at the University of Edinburgh. Formalization extent [edit] Freek Wiedijk has been keeping a ranking of proof assistants by the amount of formalized theorems out of a list of 100 well-known theorems. Notable formalized proofs Catalogues

Logically Speaking Graham Priest interviewed by Richard Marshall. Graham Priest is one of the giants of philosophical logic. He has written many books about this, including Doubt Truth to be a Liar, Towards Non-Being: the Logic and Metaphysics of Intentionality, Beyond the Limits of Thought, In Contradiction: A Study of the Transconsistent and Introduction to Non-Classical Logic. He can be found in Melbourne and New York, and sometimes in St. Andrews. 3:AM: You’re famous for denying that propositions have to be either true or false (and not both or neither) but before we get to that, can you start by saying how you became a philosopher? Graham Priest: Well, I was trained as a mathematician. 3:AM: Now, you’re interested in the very basis of how we think. GP: Well, first a clarification. 3:AM: So paraconsistent logic is a logic that tries to work out how we might formally understand treating some propositions as being both true and false at the same time. So for ‘logic’. But more should be said.

Subjective logic Subjective logic is a type of probabilistic logic that explicitly takes uncertainty and belief ownership into account. In general, subjective logic is suitable for modeling and analysing situations involving uncertainty and incomplete knowledge.[1][2] For example, it can be used for modeling trust networks and for analysing Bayesian networks. Arguments in subjective logic are subjective opinions about propositions. A binomial opinion applies to a single proposition, and can be represented as a Beta distribution. A fundamental aspect of the human condition is that nobody can ever determine with absolute certainty whether a proposition about the world is true or false. Subjective opinions[edit] Subjective opinions express subjective beliefs about the truth of propositions with degrees of uncertainty, and can indicate subjective belief ownership whenever required. where is the subject, also called the belief owner, and is the proposition to which the opinion applies. . Binomial opinions[edit]

Inference Steps in reasoning Various fields study how inference is done in practice. Human inference (i.e. how humans draw conclusions) is traditionally studied within the fields of logic, argumentation studies, and cognitive psychology; artificial intelligence researchers develop automated inference systems to emulate human inference. The process by which a conclusion is inferred from multiple observations is called inductive reasoning. This definition is disputable (due to its lack of clarity. Two possible definitions of "inference" are: A conclusion reached on the basis of evidence and reasoning.The process of reaching such a conclusion. Example for definition #1 [edit] Ancient Greek philosophers defined a number of syllogisms, correct three part inferences, that can be used as building blocks for more complex reasoning. All humans are mortal.All Greeks are humans.All Greeks are mortal. The validity of an inference depends on the form of the inference. Now we turn to an invalid form. ? (where ? ?