# Propositional Independence - Formula-Variable Independence and Forgetting

@article{Lang2003PropositionalI, title={Propositional Independence - Formula-Variable Independence and Forgetting}, author={J{\'e}r{\^o}me Lang and Paolo Liberatore and Pierre Marquis}, journal={J. Artif. Intell. Res.}, year={2003}, volume={18}, pages={391-443} }

Independence - the study of what is relevant to a given problem of reasoning - has received an increasing attention from the AI community. In this paper, we consider two basic forms of independence, namely, a syntactic one and a semantic one. We show features and drawbacks of them. In particular, while the syntactic form of independence is computationally easy to check, there are cases in which things that intuitively are not relevant are not recognized as such. We also consider the problem of…

## 229 Citations

Projection and scope-determined circumscription

- MathematicsJ. Symb. Comput.
- 2012

A Logical Study of Partial Entailment

- PhilosophyJ. Artif. Intell. Res.
- 2011

A novel logical notion-partial entailment-to propositional logic, which separates three different kinds of partial entailments and formalizes them by using an extended notion of prime implicant, and considers a potential application of partial entailsments in reasoning about rational agents.

Literal Projection for First-Order Logic

- Computer ScienceJELIA
- 2008

This work presents a formalization of literal projection and related concepts, such as literal forgetting, for first-order logic with a Herbrand semantics, which makes these notions easy to access, since they are expressed there by means of straightforward relationships between sets of literals.

On Quantifying Literals in Boolean Logic and Its Applications to Explainable AI

- Computer ScienceJ. Artif. Intell. Res.
- 2021

A novel semantics for quantification is provided, the interplay between variable/literal and existential/universal quantification, and some classes of Boolean formulas and circuits on which quantification can be done efficiently are identified.

From Explanations to Intelligible Explanations (Extended Version)

- Computer Science, Philosophy
- 2020

The stress is laid on the intelligibility issue, which concentrates a part of the difficulty of the problem, and relies on the fact that defining what a “good” explanation is does not solely concern what should be explained, but also depends on who receives the corresponding explanans.

PROJECTING SUPERFICIAL WORDS OUT

- Computer Science
- 2019

This paper uses first order logic (FOL) a classic technique from meaning representation language to explain what information is superficial for a given sentence pair and suggests two inductive biases according to its properties.

Dependence in Propositional Logic: Formula-Formula Dependence and Formula Forgetting - Application to Belief Update and Conservative Extension

- Computer ScienceAAAI
- 2018

This paper proposes two novel notions of dependence in propositional logic: formula-formula dependence and formula forgetting, which are a relation between formulas capturing whether a formula depends on another one, while the second is an operation that returns the strongest consequence independent of a formula.

A Knowledge Level Account of Forgetting

- Philosophy, Computer ScienceJ. Artif. Intell. Res.
- 2017

The central thesis is that forgetting amounts to a reduction in the language, specifically the signature, of a logic, which provides a uniform approach to forgetting, with a definition that is applicable to any logic with a well-defined consequence relation.

Knowledge Forgetting in Circumscription: A Preliminary Report

- Computer ScienceAAAI
- 2015

A theory of forgetting for propositional circumscription is proposed, which is not a straightforward adaption of existing approaches, and some properties that are essential for existing proposals do not hold any longer or have to be reformulated.

On Forgetting in Tractable Propositional Fragments

- Computer Science, PhilosophyArXiv
- 2015

A resolution-based algorithm of forgetting for CNF fragment is presented, and some complexity results about forgetting in Horn, renamable Horn, q-Horn, Krom, DNF and CNF fragments of propositional logic are presented.

## References

SHOWING 1-10 OF 67 REFERENCES

A Logical Account of Relevance

- Philosophy, Computer ScienceIJCAI
- 1995

This paper focuses on one particular area, namely relevance in the context of logical theories, and shows close connections to two others that were recently proposed, point ing to some common ground at least as far as logical relevance is concerned.

Logics of Time and Computation

- Philosophy
- 1987

Sets out the basic theory of normal modal and temporal propositional logics; applies this theory to logics of discrete (integer), dense (rational), and continuous (real) time, to the temporal logic…

Updating logical databases

- Computer ScienceCambridge tracts in theoretical computer science
- 1990

This paper presents a meta-modelling framework for model-based semantics of updates and some examples show how this framework can be applied to relational theories.

Updates, actions, and planning

- Computer ScienceIJCAI
- 2001

A new family of dependence-based update operators are given that are wellsuited to the representation of simple actions and the complexity of query entailment from an updated belief base is identified.

Updating Epistemic States

- PhilosophyAustralian Joint Conference on Artificial Intelligence
- 2001

A class of update operators are extended to epistemic states, by defining an operation playing the same role as knowledge transmutations do for belief revision, which conveys much more information than belief sets since they express the relative plausibilities of the pieces of information believed by the agent.