Second order and higher order universal decision elements in $m$-valued logic.

Boolean-Valued Second-Order Logic

Second Order Effects in Interval Valued Decision Graph Models

Second-order calculations may significantly increase a decision maker’s understanding of a decision situation when handling aggregations of imprecise representations, as is the case in decision trees or influence diagrams, while the use of only first-order results gives an incomplete picture. The results apply also to approaches which do not explicitly deal with second-order distributions, inst...

Universal Higher Order Grammar

We examine the class of languages that can be defined entirely in terms of provability in an extension of the sorted type theory (Tyn) by embedding the logic of phonologies, without introduction of special types for syntactic entities. This class is proven to precisely coincide with the class of logically closed languages that may be thought of as functions from expressions to sets of logically...

Elements of model theory in higher-order fuzzy logic

In this paper, we turn our attention to model theory of higher-order fuzzy logic (fuzzy type theory). This theory generalizes model theory of predicate logic but has some interesting specificities. We will introduce few basic concepts related to homomorphism, isomorphism, submodel, etc. and show some properties of them.

khunaji’s tautologies in second-order logic

for the first time in the history of logic, afzal al-din al-khunaji has found tautologies and contradictories among the verity and actuality propositions. these have been formalized and investigated in first-order logic and it has been shown that their perpetual truth requires the assumption of ‘the presupposed existence of non-existence.’ in this paper, i investigate the tautologies in second-...