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...]], aggregates (counting, summing, maximising ... over a set), arithmetic, inductive definitions, partial functions, and intensional objects. ...information", to be used as input to various generic reasoning algorithms. Reasoning engines that use FO(.) include IDP-Z3,<ref>{{cite web |url=http://www.idp-z ...

...learning action models differs from [[reinforcement learning]]. It enables reasoning about actions instead of expensive trials in the world.<ref name="amir2008" </ref> Action model learning is a form of [[inductive reasoning]], where new knowledge is generated based on agent's ''observations''. It d ...

...by [[John Alan Robinson]] in 1965 and has become a fundamental notion in [[inductive logic programming]]. Deciding whether a given clause θ-subsumes another is ...lution (logic)|resolution]],{{sfn|Robinson|1965}} and was first applied to inductive logic programming by [[Gordon Plotkin]] in 1970 for finding and reducing le ...

...>ID_\nu</math> are referred to as "the formal theories of ν-times iterated inductive definitions". ID_ν extends [[Peano axioms|PA]] by ν iterated leas To define the system of ν-times iterated inductive definitions, where ν is an ordinal, let <math>\prec</math> be a primitive r ...

...mathematical [[probability theory]], such as [[Bayes' theorem]], and of [[inductive logic]].<ref name="veritas">{{cite web |url=https://www.youtube.com/watch?v ...ter book ''[[Is There a God?]]'', omitting the use of Bayes' theorem and [[inductive logic]], but including a discussion of [[many-worlds interpretation|multipl ...

...ines classical [[predicate logic]] and [[probability theory]] ([[Inductive reasoning#Bayesian inference|Bayesian inference]]). Probability values are assigned t ...ive Logic and Probability'', Volume 1, pp 69-70.</ref> and the modern Pure Inductive Logic evolves along the lines of the pure, uninterpreted approach envisaged ...

...1007-3-540-45402-0/page/n396 383]|title=Logic Programming and Nonmonotonic Reasoning: 6th International Conference, LPNMR 2001, Vienna, Austria, September 17-19 ...'''A''', '''F''' a set of functions in '''A''', and <math> X_+ </math> the inductive closure of '''X''' under '''F'''. ...

...y]] of future events based on past events. It is the basis for [[inductive reasoning]], and gives the mathematical basis for [[learning]] and the perception of ...l programs that generate strings starting with ''x''. Cast in the form of inductive inference, the programs are theories that imply the observation of the bit ...

...however, may include the [[inductive reasoning|inductive]] and [[abductive reasoning|abductive]] modes of proof.<ref name="Pedemont07">{{cite journal |last1=Ped ...however, can never prove that the hypotheses (h) is true, but relies on an inductive inference by measuring the probability of the hypotheses relative to the em ...

...tructured prediction include [[inductive logic programming]], [[case-based reasoning]], [[structured SVM]]s, [[Markov logic network]]s, [[Probabilistic Soft Log ...

...hese unsolved problems act as exam questions. In the [[Inductive reasoning|inductive]] setting, they become practice problems of the sort that will make up the ...given unlabeled data <math>x_{l+1},\dots,x_{l+u}</math> only. The goal of inductive learning is to infer the correct mapping from <math>X</math> to <math>Y</ma ...

...cess=free }}</ref> It is based on the [[calculus of constructions]] with [[inductive type]]s. It is an [[open-source]] project hosted on [[GitHub]]. It was deve The [[natural numbers]] can be defined as an [[inductive type]]. This definition is based on the [[Peano axioms]] and states that ev ...

...971">{{cite journal|first1=Gordon D.|last1=Plotkin|title=A Further Note on Inductive Generalization|editor1-first=B.|editor1-last=Meltzer|editor2-first=D.|edito ...rder logic, which was the basis of the [[Golem (ILP)|Golem]] approach to [[inductive logic programming]]. ...

...k|first2 = G.|last3 = De Raedt|first3 = L.|title = An algebraic Prolog for reasoning about possible worlds|conference = Proceedings of the Twenty-Fifth AAAI Con ...id|chapter = The independent choice logic and beyond|title = Probabilistic Inductive Logic Programming| series=Lecture Notes in Computer Science |date = 2008|pa ...

...rk with an arbitrary number of [[Node (circuits)|nodes]] by an [[Inductive reasoning|induction argument]]. A linear network can be represented as a set of line ...

...mathematics]] which rejects the [[law of excluded middle]] in mathematical reasoning. ...en symbol string). Poincaré (1905) asserted that, by doing this, Hilbert's reasoning became circular.<ref>van Heijenoort's commentary on Weyl (1927).</ref> Weyl ...

...e [[constraint (mathematics)|constraint]]s. It also relates to [[inductive reasoning]] in modeling and decision-making. The technique has existed for decades as ...

...does not postulate any restrictions on the syntactic form of definitions. Inductive definitions require their ''definientia'' to be ''positive'', in the sense is acceptable in revision theory, although not in the theory of inductive definitions. ...

}}</ref> '''of algebraic value sets''' gives a method of reasoning about the values in unsolved or partially solved equations. Where logic pr ...d on initial probabilities given by [[#Boolean inductive inference|Boolean inductive inference]]. ...

===The univalence axiom, synthetic homotopy theory, and higher inductive types=== ...things to come out of the Oberwolfach meeting was the basic idea of higher inductive types, due to Lumsdaine, Shulman, Bauer, and Warren. The participants also ...