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The second-order logic without these restrictions is sometimes called full second-order logic to distinguish it from the monadic version. Monadic second-order logic is particularly used in the context of Courcelle's theorem, an algorithmic meta-theorem in graph theory. The MSO theory of the complete infinite binary tree is decidable.
This solution is inconsistent with experimental evidence, which finds that most players choose numbers around either 25 or 13. These guesses are consistent with first- and second-order depth of reasoning, supporting CHT. A small proportion of players exhibit depths of reasoning greater than second order. [6] [4]
that between first-order and second-order investigations. Some authors say that philosophical inquiry is second-order, having concepts, theories and presupposition as its subject matter; that it is "thinking about thinking", of a "generally second-order character"; [ 30 ] that philosophers study, rather than use, the concepts that structure our ...
Second-order cybernetics took shape during the late 1960s and mid 1970s. The 1967 keynote address to the inaugural meeting of the American Society for Cybernetics (ASC) by Margaret Mead, who had been a participant at the Macy Conferences, is a defining moment in its development.
[2]: 13 In later writings, Cabrera describes D, S, R, and P as "patterns of thinking", and expands upon the implications of these thinking skills. [ 3 ] [ 4 ] The DSRP theory is a mathematical formalism of systems thinking and cognition , built on the philosophical underpinnings of constructivism and evolutionary epistemology .
In the monadic second-order logic of graphs, the variables represent objects of up to four types: vertices, edges, sets of vertices, and sets of edges. There are two main variations of monadic second-order graph logic: MSO 1 in which only vertex and vertex set variables are allowed, and MSO 2 in which all four types of variables are allowed ...
A second-order propositional logic is a propositional logic extended with quantification over propositions. A special case are the logics that allow second-order Boolean propositions , where quantifiers may range either just over the Boolean truth values , or over the Boolean-valued truth functions .
In addition to Fagin's 1974 paper, [1] the 1999 textbook by Immerman provides a detailed proof of the theorem. [4] It is straightforward to show that every existential second-order formula can be recognized in NP, by nondeterministically choosing the value of all existentially-qualified variables, so the main part of the proof is to show that every language in NP can be described by an ...