Inference. Inference is the act or process of deriving logical conclusions from premises known or assumed to be true.[1] The conclusion drawn is also called an idiomatic. The laws of valid inference are studied in the field of logic. Alternatively, inference may be defined as the non-logical, but rational means, through observation of patterns of facts, to indirectly see new meanings and contexts for understanding. Of particular use to this application of inference are anomalies and symbols. Inference, in this sense, does not draw conclusions but opens new paths for inquiry. (See second set of Examples.) Human inference (i.e. how humans draw conclusions) is traditionally studied within the field of cognitive psychology; artificial intelligence researchers develop automated inference systems to emulate human inference.
Statistical inference uses mathematics to draw conclusions in the presence of uncertainty. Examples[edit] All men are mortalSocrates is a manTherefore, Socrates is mortal. ? (where ? ? P. 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. " See also[edit] References[edit] T. 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. Inductive reasoning. Inductive reasoning (as opposed to deductive reasoning or abductive reasoning) is reasoning in which the premises seek to supply strong evidence for (not absolute proof of) the truth of the conclusion. While the conclusion of a deductive argument is certain, the truth of the conclusion of an inductive argument is probable, based upon the evidence given.[1] The philosophical definition of inductive reasoning is more nuanced than simple progression from particular/individual instances to broader generalizations. Rather, the premises of an inductive logical argument indicate some degree of support (inductive probability) for the conclusion but do not entail it; that is, they suggest truth but do not ensure it. In this manner, there is the possibility of moving from general statements to individual instances (for example, statistical syllogisms, discussed below).
Description[edit] Inductive reasoning is inherently uncertain. An example of an inductive argument: For example: Criticism[edit] 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]
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 multinomial opinion applies to a collection of propositions, and can be represented as a Dirichlet distribution. Through the correspondence between opinions and Beta/Dirichlet distributions, subjective logic provides an algebra for these functions. Opinions are also related to the belief functions of Dempster-Shafer belief theory.
Subjective opinions[edit] where is the subject, also called the belief owner, and is the proposition to which the opinion applies. . Let where: and . . .
Knowledge representation and reasoning. Knowledge representation and reasoning (KR) is the field of artificial intelligence (AI) devoted to representing information about the world in a form that a computer system can utilize to solve complex tasks such as diagnosing a medical condition or having a dialog in a natural language. Knowledge representation incorporates findings from psychology about how humans solve problems and represent knowledge in order to design formalisms that will make complex systems easier to design and build. Knowledge representation and reasoning also incorporates findings from logic to automate various kinds of reasoning, such as the application of rules or the relations of sets and subsets.
Examples of knowledge representation formalisms include semantic nets, Frames, Rules, and ontologies. Examples of automated reasoning engines include inference engines, theorem provers, and classifiers. Overview[edit] This hypothesis was not always taken as a given by researchers. History[edit] Characteristics[edit] Reason. Psychologists and cognitive scientists have attempted to study and explain how people reason, e.g. which cognitive and neural processes are engaged, and how cultural factors affect the inferences that people draw. The field of automated reasoning studies how reasoning may or may not be modeled computationally. Animal psychology considers the question of whether animals other than humans can reason. Etymology and related words[edit] In the English language and other modern European languages, "reason", and related words, represent words which have always been used to translate Latin and classical Greek terms in the sense of their philosophical usage.
The original Greek term was "λόγος" logos, the root of the modern English word "logic" but also a word which could mean for example "speech" or "explanation" or an "account" (of money handled).[7]As a philosophical term logos was translated in its non-linguistic senses in Latin as ratio. Philosophical history[edit] Classical philosophy[edit]