Anna Zamansky

FLAP Journal 2019 Journal Article

Preface.

• Ofer Arieli
• Anna Zamansky

FLAP Journal 2017 Journal Article

Teaching Logic to Information Systems Student: A Student-centric Approach.

• Anna Zamansky

JELIA Conference 2012 Conference Paper

A Preferential Framework for Trivialization-Resistant Reasoning with Inconsistent Information

• Anna Zamansky

Abstract Paraconsistent entailments based on more than two truth-values are useful formalisms for handling inconsistent information in large knowledge bases. However, such entailments suffer from two major drawbacks: they are often too cautious to allow intuitive classical inference, and are trivialization-prone. Two preferential mechanisms have been proposed to deal with these two problems, but they are formulated in different terms, and are hard to combine. This paper is a step towards a systematization and generalization of these approaches. We define an abstract framework, which allows for incorporating various preferential criteria into paraconsistent entailments in a modular way. We show that many natural cases of previously studied entailments can be simulated within this framework. Its usefulness is also demonstrated using a concrete domain related to ancient geography.

IJCAI Conference 2011 Conference Paper

What Is an Ideal Logic for Reasoning with Inconsistency?

• Ofer Arieli
• Arnon Avron
• Anna Zamansky

Many AI applications are based on some underlying logic that tolerates inconsistent information in a non-trivial way. However, it is not always clear what should be the exact nature of such a logic, and how to choose one for a specific application. In this paper, we formulate a list of desirable properties of `ideal' logics for reasoning with inconsistency, identify a variety of logics that have these properties, and provide a systematic way of constructing, for every n > 2, a family of such n-valued logics.

KR Conference 2010 Conference Paper

Maximally Paraconsistent Three-Valued Logics

• Ofer Arieli
• Arnon Avron
• Anna Zamansky

Maximality is a desirable property of paraconsistent logics, motivated by the aspiration to tolerate inconsistencies, but at the same time retain from classical logic as much as possible. In this paper, we introduce the strongest possible notion of maximal paraconsistency, and investigate it in the context of logics that are based on deterministic or non-deterministic three-valued matrices. We first show that most of the logics that are based on properly non-deterministic three-valued matrices are not maximally paraconsistent. Then we show that in contrast, in the deterministic case all the natural three-valued paraconsistent logics are maximal. This includes well-known three-valued paraconsistent logics like P1, LP, J3, PAC and SRM3, as well as any extension of them obtained by enriching their languages with extra three-valued connectives. In this paper, we investigate strong maximality of paraconsistent logics based on three-valued deterministic and non-deterministic matrices. The former are one of the oldest and most common ways of defining a paraconsistent logic. The latter are a recent natural generalization of the former, introduced in (Avron and Lev 2005), in which nondeterministic interpretations of connectives are allowed. Under a very minimal and natural assumption about the interpretation of negation in these matrices, we show that in the deterministic case, all natural three-valued paraconsistent logics are maximal in the strong sense. Our result applies to such well-known paraconsistent logics as Sette’s logic P1, Priest’s LP, the semi-relevant logic SRM3, the logics PAC and J3, and any extension of one of these logics obtained by enriching its language with extra three-valued connectives. 1 In the non-deterministic case things are quite different, though. We show that paraconsistent logics induced by properly non-deterministic three-valued matrices are usually not maximal, except for a few special cases (which are fully characterized). However, even these exceptional cases are redundant, as we show that any maximally paraconsistent logic defined by an n-valued non-deterministic matrix can be fully characterized also by a deterministic one.

JELIA Conference 2010 Conference Paper

Similarity-Based Inconsistency-Tolerant Logics

• Ofer Arieli
• Anna Zamansky

Abstract Many logics for AI applications that are defined by denotational semantics are trivialized in the presence of inconsistency. It is therefore often desirable, and practically useful, to refine such logics in a way that inconsistency does not cause the derivation of any formula, and, at the same time, inferences with respect to consistent premises are not affected. In this paper, we introduce a general method of doing so by incorporating preference relations defined in terms of similarities. We exemplify our method for three of the most common denotational semantics (standard many-valued matrices, their non-deterministic generalization, and possible worlds semantics), and demonstrate their usefulness for reasoning with inconsistency.

KR Conference 2006 Conference Paper

Non-deterministic semantics for first-order paraconsistent logics

• Arnon Avron
• Anna Zamansky

Using non-deterministic structures called Nmatrices, we provide simple modular non-deterministic semantics for a large family of first-order paraconsistent logics with a formal consistency operator, also known as LFIs. This includes da-Costa's well known predicate calculus C*1. We show how consistency propagation in quantified formulas is captured in the semantic framework of Nmatrices, and analyze the semantic effects of different styles of propagation considered in the literature of LFIs. Then we demonstrate how the tool of Nmatrices can be applied to prove a non-trivial property of first-order LFIs discussed in this paper.