DeepAI AI Chat
Log In Sign Up

Proof Search on Bilateralist Judgments over Non-deterministic Semantics

by   Vitor Greati, et al.

The bilateralist approach to logical consequence maintains that judgments of different qualities should be taken into account in determining what-follows-from-what. We argue that such an approach may be actualized by a two-dimensional notion of entailment induced by semantic structures that also accommodate non-deterministic and partial interpretations, and propose a proof-theoretical apparatus to reason over bilateralist judgments using symmetrical two-dimensional analytical Hilbert-style calculi. We also provide a proof-search algorithm for finite analytic calculi that runs in at most exponential time, in general, and in polynomial time when only rules having at most one formula in the succedent are present in the concerned calculus.


page 1

page 2

page 3

page 4


Finite two-dimensional proof systems for non-finitely axiomatizable logics

The characterizing properties of a proof-theoretical presentation of a g...

A polynomial time algorithm for the Lambek calculus with brackets of bounded order

Lambek calculus is a logical foundation of categorial grammar, a linguis...

Monadicity of Non-deterministic Logical Matrices is Undecidable

The notion of non-deterministic logical matrix (where connectives are in...

A Logical Study of Partial Entailment

We introduce a novel logical notion--partial entailment--to propositiona...

Computational Aspects of the Calculus of Structure

Logic is the science of correct inferences and a logical system is a too...

A Deterministic Algorithm for the Capacity of Finite-State Channels

We propose a modified version of the classical gradient descent method t...