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A wide range of intuitionistic type theories may be presented as equational theories within a logical framework. This method was formulated by Per Martin-L{o}f in the mid-1980s and further developed by Uemura, who used it to prove an initiality result for a class of models. Herein is presented a logical framework for type theories that includes an extensional equality type so that a type theory may be given by a signature of constants. The framework is illustrated by a number of examples of type-theoretic concepts, including identity and equality types, and a hierarchy of universes.
An equational axiomatisation of probability functions for one-dimensional event spaces in the language of signed meadows is expanded with conditional values. Conditional values constitute a so-called signed vector meadow. In the presence of a probabi
Cubical type theory provides a constructive justification of homotopy type theory. A crucial ingredient of cubical type theory is a path lifting operation which is explained computationally by induction on the type involving several non-canonical cho
Appel and McAllesters step-indexed logical relations have proven to be a simple and effective technique for reasoning about programs in languages with semantically interesting types, such as general recursive types and general reference types. Howeve
We study the computational complexity of satisfiability problems for classes of simple finite height (ortho)complemented modular lattices $L$. For single finite $L$, these problems are shown tobe $mc{NP}$-complete; for $L$ of height at least $3$, equ
We prove that $omega$-regular languages accepted by Buchi or Muller automata satisfy an effective automata-theoretic version of the Baire property. Then we use this result to obtain a new effective property of rational functions over infinite words w