DeepAI AI Chat
Log In Sign Up

Proof search for full intuitionistic propositional logic through a coinductive approach for polarized logic

07/31/2020
by   José Espírito Santo, et al.
0

The approach to proof search dubbed "coinductive proof search", and previously developed by the authors for implicational intuitionistic logic, is in this paper extended to polarized intuitionistic logic. As before, this includes developing a coinductive description of the search spaces generated by a sequent, an equivalent inductive syntax describing the same space, and decision procedures for inhabitation problems in the form of predicates defined by recursion on the inductive syntax. The polarized logic can be used as a platform from which proof search for other logics is understood. We illustrate the technique with LJT, a focused sequent calculus for full intuitionistic propositional logic (including disjunction). For that, we have to work out the "negative translation" of LJT into the polarized logic (that sees all intuitionistic types as negative types), and verify that the translation gives a faithful representation of proof search in LJT as proof search in the polarized logic.

READ FULL TEXT

page 1

page 2

page 3

page 4

07/11/2012

LPC(ID): A Sequent Calculus Proof System for Propositional Logic Extended with Inductive Definitions

The logic FO(ID) uses ideas from the field of logic programming to exten...
02/22/2022

A Heuristic Proof Procedure for Propositional Logic

Theorem proving is one of the oldest applications which require heuristi...
07/16/2021

Countability of Inductive Types Formalized in the Object-Logic Level

The set of integer number lists with finite length, and the set of binar...
01/08/2021

A Rewriting Logic Approach to Specification, Proof-search, and Meta-proofs in Sequent Systems

This paper develops an algorithmic-based approach for proving inductive ...
06/20/2017

Towards Proof Synthesis Guided by Neural Machine Translation for Intuitionistic Propositional Logic

Inspired by the recent evolution of deep neural networks (DNNs) in machi...
05/08/2014

Dialogues for proof search

Dialogue games are a two-player semantics for a variety of logics, inclu...
10/16/2020

Focused Proof-search in the Logic of Bunched Implications

The logic of Bunched Implications (BI) freely combines additive and mult...