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A Unifying Approach for Nonmonotonic S4F, (Reflexive) Autoepistemic Logic, and Answer Set Programming

Su Ezgi Iraz

Fundamenta Informaticae

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2020

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Vol. 176, nr 3/4

205--234

EN

This paper presents a general strategy, bringing together some major types of nonmonotonic reasoning under a monotonic bimodal setting. Such formalisms are also of interest to the fields of knowledge representation and declarative programming. We exemplify the methodology, capturing minimal model reasoning that underlies nonmonotonicity over S4F first, but then we also show how to apply the technique to other nonmonotonic logics respectively based on the modal logics KD45 and SW5 . We naturally succeed it, by modifying only the axioms of the underlying modal logic and show that it successfully works. The last two formalisms are also known as autoepistemic logic (AEL) and its reflexive extension (RAEL) in the given order: AEL is an important form of nonmonotonic reasoning, introduced by Robert C. Moore in order to allow an agent to reason about his own knowledge. Equilibrium logic (EL) is a general-purpose nonmonotonic reasoning formalism, proposed more recently by David Pearce as a semantical framework for answer set programming (ASP). The latter is an efficient declarative problem solving approach with lots of applications to science and technology. Fariñas et al. have embedded EL (and so ASP) into a monotonic bimodal logic. We take this work as an initiative and successfully apply a similar methodology to closely aligned nonmonotonic modal logics. We finally discuss the potential capability to subsume the epistemic extensions of ASP within our unified paradigm.

2

Towards a Rational Closure for Expressive Description Logics : the Case of SHIQ

Giordano L., Gliozzi V., Olivetti N.

Fundamenta Informaticae

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2018

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Vol. 159, nr 1/2

95--122

EN

We explore the extension of the notion of rational closure to logics lacking the finite model property, considering the logic SHIQ. We provide a semantic characterization of rational closure in SHIQ in terms of a preferential semantics, based on a finite rank characterization of minimal models. We show that the rational closure of a KB can be computed in EXPTIME based on a polynomial encoding of the rational extension of SHIQ into entailment in SHIQ. We discuss the extension of rational closure to more expressive description logics.

3

Revision of Ontologies to Accommodate Exceptions : a Typicality-based Approach

Micalizio R., Pozzato G. L.

Fundamenta Informaticae

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2018

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Vol. 161, nr 1/2

163--189

EN

The paper presents a methodology to revise a Description Logic knowledge base when exceptions are detected. The approach exploits concepts and results from techniques developed for debugging Description Logic terminologies. Debugging an inconsistent terminology amounts to identifying a minimal subset of axioms responsible for the inconsistency (i.e., an error to be removed by a knowledge engineer). Exception handling, instead, requires to revise the axioms causing an inconsistency so that a new consistent knowledge base is obtained, encompassing the detected exception about an individual x. To this aim, we make use of a nonmonotonic extension of the Description Logic ALC based on the combination of a typicality operator and the well established nonmonotonic mechanism of rational closure, which allows one to deal with prototypical properties and defeasible inheritance.

4

Multi-Party Persuasion : a Paraconsistent Approach

Dunin-Kęplicz B., Powała A.

Fundamenta Informaticae

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2018

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Vol. 158, nr 1/3

1--39

EN

Some conflicts appearing in multi-agent settings may be resolved via communication. In this paper, besides conflicts of opinions, paradigmatically resolved by a persuasion dialogue, we study semantically deeper conflicts reaching to motivations of opinions. This investigation led us to discerning deep persuasion dialogues aiming at the resolution of conflicting motivations of opinions. In our overall research program we focus on realistic modeling of agency. This includes a proper representation of agents' ignorance and inconsistencies, appearing in their informational stance. Therefore, our formal framework TalkLOG, designed to provide and embed different forms of dialogues, employs a 4-valued logic with two additional logical values, unknown and inconsistent. Within TalkLOG soundness and completeness of persuasion was proved by comparing the outcomes of the persuasion dialogues performed by n-agents with the outcomes obtained by merging knowledge of these n agents. In this context the key point was a proper construction of this merge operator. Another critical issue is complexity of agents' communication, which is typically interleaved with reasoning in the context of multi-agent or autonomous systems. In TalkLOG tractability of both aspects is obtained thanks to the implementation tool: rule-based 4-valued query language 4QL.

5

An axiomatization of Wansing's expansion of Nelson's logic

Omori H.

Reports on Mathematical Logic

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2015

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Vol. 50

41--51

EN

The present note offers an axiomatization for an expansion of Nelson’s logic motivated by Heinrich Wansing which serves as a base logic for the framework of nonmonotonic reasoning considered by Dov Gabbay and Raymond Turner. We also show that the expansion of Wansing is not conservative over intuitionistic logic, but at least as strong as Jankov’s logic.

6

Negatywna informacja w języku regułowym 4QL

Małuszyński J., Szałas A.

Zeszyty Naukowe Warszawskiej Wyższej Szkoły Informatyki

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2013

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nr 9

7--14

EN

Problematyka negatywnej informacji w językach regułowych jest zasadnicza z punktu widzenia dużej liczby aplikacji. Była ona rozważana w rozszerzeniach języków zapytań w dedukcyjnych bazach danych, opartych na wnioskowaniach niemonotonicznych, początkowo wynikających z założenia o zamkniętym świecie CWA (Closed World Assumption). W wielu zastosowaniach, w tym związanych z Semantycznym Internetem i robotyką, założenie CWA nie jest właściwe i zwykle przyjmuje się w nich założenie o świecie otwartym OWA (Open World Assumption). W niniejszym artykule omawiamy nowe podejście do tego problemu, przedstawione w [2] [3] [4], gdzie zaproponowaliśmy język regułowy 4QL w stylu Datalogu, jednak bez ograniczeń na wystąpienie negacji. Język ma architekturę warstwową. Najniższe warstwy 4QL, oparte na OWA, są w pełni monotoniczne. W celu zmniejszenia stref niewiedzy/sprzeczności w [2] [3] wprowadzono proste konstrukcje pozwalające na wyrażanie mechanizmów wnioskowań niemonotonicznych, w tym umożliwiających rozwiązywanie sprzeczności, użycie lokalnych domknięć świata (a więc także CWA) oraz różnych form wnioskowań przez domniemania. Obliczanie zapytań w 4QL ma złożoność wielomianową ze względu na rozmiar bazy danych.

XX

The problem of negative information in rule languages is crucial in many applications. It has been addressed in extensions of query languages in deductive databases, based on nonmonotonic logics initially derived from the Closed World Assumption (CWA). In many applications, including Semantic Web technologies and robotics systems, CWA is not necessarily applicable and developments in these fields usually follow the Open World Assumption (OWA). In this paper we summarize a novel approach to the problem reported in [2] [3] [4], where we proposed a DATALOG-like language 4QL with unrestricted negation. The language supports a layered architecture. The monotonic layer of 4QL, based on OWA, is fully monotonic. To reduce the unknown/inconsistent zones, in [2] [3] we have introduced simple constructs which allow one to express various mechanisms of nonmonotonic reasoning. In particular, this provides means for application-specific disambiguation of inconsistent information, the use of Local CWA (thus also CWA, if needed), and various forms of default reasoning. Query evaluation in 4QL is still tractable as regards its data complexity.