Equivalents of the finitary non-deterministic inductive definitions
نویسندگان
چکیده
منابع مشابه
Non-deterministic inductive definitions
We study a new proof principle in the context of constructive ZermeloFraenkel set theory based on what we will call “non-deterministic inductive definitions”. We give applications to formal topology as well as a predicative justification of this principle.
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We describe how the calculus of partial inductive definitions is used to represent logics. This calculus includes the powerful principle of definitional reflection. We describe two conceptually different approaches to representing a logic, both making essential use of definitional reflection. In the deductive approach, the logic is defined by its inference rules. Only the succedent rules (in a ...
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We present a principle for introducing new types in type theory which generalises strictly positive indexed inductive data types. In this new principle a set A is defined inductively simultaneously with an A-indexed set B, which is also defined inductively. Compared to indexed inductive definitions, the novelty is that the index set A is generated inductively simultaneously with B. In other wor...
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Well-known principles of induction include monotone induction and different sorts of nonmonotone induction such as inflationary induction, induction over well-founded sets and iterated induction. In this work, we define a logic formalizing induction over well-founded sets and monotone and iterated induction. Just as the principle of positive induction has been formalized in FO(LFP), and the pri...
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In formal verification, inductive definitions of predicates are widely used when we define recursive notions and algorithms. In actual verification, we often introduce a new inductively defined predicate by modifying an existing inductive definition. In such a case, it is usual that there are some relationships between two predicates, and such relationship theorems make the properties on one pr...
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ژورنال
عنوان ژورنال: Annals of Pure and Applied Logic
سال: 2019
ISSN: 0168-0072
DOI: 10.1016/j.apal.2019.05.005