Natural Deduction Bottom Up

Bottom-Up Earley Deduction

We propose a bottom-up variant of Earley deduction. Bottom-up deduction is preferable to top-down deduction because it allows incrementai processing (even for head-driven grammars), it is data-driven, no subsumption check is needed, and preference values attached to lexical items can be used to guide best-first search. We discuss the scanning step for bottom-up Earley deduction and indexing sch...

Abductive language interpretation as bottom-up deduction

A translation of abductive language interpretation problems into a deductive form is proposed and shown to be correct. No meta-level overhead is involved in the resulting formulas that can be evaluated by bottom-up deduction, e.g., by considering them as Constraint Handling Rules. The problem statement may involve background theories with integrity constraints, and minimal contexts are produced...

Bidirectional Natural Deduction

The goal of this paper is to present a theorem prover able to perform both forward and backward reasoning supported by a well deened formal system. This system for bidirectional reasoning has been proved equivalent to Gentzen's classical system of propositional natural deduction. This paper, primarily aimed at developing a deeper theoretical understanding of bidirectional reasoning, provides ba...

Focused Natural Deduction

Natural deduction for intuitionistic linear logic is known to be full of non-deterministic choices. In order to control these choices, we combine ideas from intercalation and focusing to arrive at the calculus of focused natural deduction. The calculus is shown to be sound and complete with respect to first-order intuitionistic linear natural deduction and the backward linear focusing calculus.

Aristotle'S natural deduction reconsidered