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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.
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.
The second order objects are arbitrary sets (or unary predicates) of finite binary strings. S2S has functions s→s0 and s→s1 on strings, and predicate s∈S (equivalently, S(s)) meaning string s belongs to set S. Some properties and conventions: By default, lowercase letters refer to first order objects, and uppercase to second order objects.
[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 .
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 .
A subsystem of second-order arithmetic is a theory in the language of second-order arithmetic each axiom of which is a theorem of full second-order arithmetic (Z 2). Such subsystems are essential to reverse mathematics , a research program investigating how much of classical mathematics can be derived in certain weak subsystems of varying strength.
Second order approximation, an approximation that includes quadratic terms; Second-order arithmetic, an axiomatization allowing quantification of sets of numbers; Second-order differential equation, a differential equation in which the highest derivative is the second; Second-order logic, an extension of predicate logic
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 ...