Intuitionistic logic and modal logic each admit meaningful projections of classical theories. While intuitionistic logic can interpret classical logic by a host of translations, thus yielding computational interpretations, modal logic can be employed to understand notions of provability and truth. However, the enrichment of intuitionistic logic by modalities is far less canonical than its classical…
Anupam Das
Deterministic – nondeterministic pairs in proof theory
This is meant to be a light post, posing a perhaps naive question. One of the hallmarks of computational proof theory is the association between arithmetic theories and complexity classes, in terms of their provably recursive functions. But is there a general rule for identifying the provably recursive functions of a class of induction invariants?
‘Simple’ proofs of cut-elimination II: intuitionistic logic
Cut-elimination for intuitionistic logic has particular significance to proof theorists due to the constructive nature of the logic. Cut-free proofs give rise to significant computational information, including interpolants of implications and, in the case of predicate logic, witnesses of existentials. Moreover, the process of cut-elimination can itself be viewed as a computational process thanks to…
A new linear inference of size 8
Linear inferences are propositional tautologies of the form , where and are formulas with at most one occurrence of each propositional variable. These form a -complete set, but surprisingly little is known about their structure, despite their importance in structural proof theory (and beyond). In this post I will cover some of the background on…
