Prominent constructive theories of sets such as Martin-L¨of type theory and Aczel and Myhill constructive set theory, feature a distinctive form of constructivity: predicativity. This may be phrased…
Some remarks about Dependent Type Theory
- Computer Science
One main theme of this work is the importance of notations in mathematics and computer science: new questions were asked and solved only because of the use of AUTOMATH notation, itself a variation of λ-notation introduced by A. Church for representing functions.
INCOMPLETENESS VIA PARADOX AND COMPLETENESS
- PhilosophyThe Review of Symbolic Logic
A generalization of the Arithmetized Completeness Theorem is presented whereby Russell’s paradox, a variant of Mirimanoff's paradox, the Liar, and the Grelling–Nelson paradox may be uniformly transformed into incompleteness theorems.
Wittgenstein’s Tractatus Logico-Philosophicus and a Hierarchical Approach to Solving Logical Paradoxes
- PhilosophyFilosofija. Sociologija
The hierarchical approach to the solution of logical paradoxes is considered in the article. The foundations and main theses of the hierarchical approach are analysed through consideration of…
In Praise of Impredicativity: A Contribution to the Formalization of Meta-Programming
- Computer ScienceTheory and Practice of Logic Programming
Reflective Predicate Logic is defined, a conservative extension of first-order logic, which provides a simple formalization of meta-programming.
Predicativity and Feferman
Predicativity is a notable example of fruitful interaction between philosophy and mathematical logic. It originated at the beginning of the 20th century from methodological and philosophical…
All There Is: On the Semantics of Quantification over Absolutely Everything
All There Is: On the Semantics of Quantification over Absolutely Everything is a treatise on semantics over absolutely everything.
Logic Programming and Nonmonotonic Reasoning
- Computer ScienceLecture Notes in Computer Science
A novel feature of this competition edition is the re-introduction of a Model&Solve track, complementing the usual System track with problem domains where participants need to provide dedicated encodings and solving means.