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Szalas, Andrzej
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De Angelis, F. L., Di Marzo Serugendo, G. & Szalas, A. (2018). Paraconsistent Rule-Based Reasoning with Graded Truth Values. Journal of Applied Logic, 5(1), 185-220
Open this publication in new window or tab >>Paraconsistent Rule-Based Reasoning with Graded Truth Values
2018 (English)In: Journal of Applied Logic, ISSN 2055-3706, Vol. 5, no 1, p. 185-220Article in journal (Refereed) Published
Abstract [en]

Modern artificial systems, such as cooperative traffic systems or swarm robotics, are made of multiple autonomous agents, each handling uncertain, partial and potentially inconsistent information, used in their reasoning and decision making. Graded reasoning, being a suitable tool for addressing phenomena related to such circumstances, is investigated in the literature in many contexts – from graded modal logics to various forms of approximate reasoning. In this paper we first introduce a family of many-valued paraconsistent logics parametrised by a number of truth/falsity/inconsistency grades allowing one to handle multiple truth-values at the desired level of accuracy. Second, we define a corresponding family of rule-based languages with graded truth-values as first-class citizens, enjoying tractable query evaluation. In addition, we introduce introspection operators allowing one to resolve inconsistencies and/or lack of information in a non-monotonic manner. We illustrate and discuss the use of the framework in an autonomous robot scenario.

Place, publisher, year, edition, pages
College Publications, 2018
National Category
Computer Sciences
Identifiers
urn:nbn:se:liu:diva-153434 (URN)
Available from: 2018-12-14 Created: 2018-12-14 Last updated: 2018-12-19Bibliographically approved
Doherty, P. & Szalas, A. (2018). Signed Dual Tableaux for Kleene Answer Set Programs. In: Golińska-Pilarek J., Zawidzki M. (Ed.), Ewa Orłowska on Relational Methods in Logic and Computer Science: (pp. 233-252). Cham: Springer
Open this publication in new window or tab >>Signed Dual Tableaux for Kleene Answer Set Programs
2018 (English)In: Ewa Orłowska on Relational Methods in Logic and Computer Science / [ed] Golińska-Pilarek J., Zawidzki M., Cham: Springer, 2018, p. 233-252Chapter in book (Refereed)
Abstract [en]

Dual tableaux were introduced by Rasiowa and Sikorski (1960) as a cut free deduction system for classical first-order logic. In the current paper, a sound and complete proof procedure based on dual tableaux is proposed for

R3

which is the standard Kleene logic augmented with a weak negation connective and an implication connective proposed, in another context, by Shepherdson (1989).

R3

is used as a basis for defining Kleene Answer Set Programs (

ASPK

programs). The semantics for

ASPK

programs is based on strongly supported models. Both entailment procedures and model generation procedures for normal and non-normal

ASPK

programs are proposed based on the use of dual tableaux and a model filtering technique. The dual tableau proof procedure extended with a model filtering technique is shown to be sound and complete for

ASPK

programs, both normal and non-normal. Since there is a direct relationship between answer sets for classical ASP programs and

R3

models for

ASPK

programs, it can be shown that the sound and complete dual tableaux proof procedure with filtering for ASPK" role="presentation">ASPKprograms is also sound and complete for classical normal ASP programs. For classical non-normal ASP programs, the proof procedure is only sound, since an alternative semantics for disjunction is used in

ASPK

Place, publisher, year, edition, pages
Cham: Springer, 2018
Series
Outstanding Contributions to Logic ; 17
Keywords
Signed tableaux, Signed dual tableaux, Answer set programming, Kleene three-valued logic, Strongly supported model
National Category
Computer Sciences
Identifiers
urn:nbn:se:liu:diva-153431 (URN)10.1007/978-3-319-97879-6_9 (DOI)9783319978789 (ISBN)9783319978796 (ISBN)
Available from: 2018-12-14 Created: 2018-12-14 Last updated: 2019-01-10Bibliographically approved
Bialek, L., Dunin-Keplicz, B. & Szalas, A. (2018). Towards a Paraconsistent Approach to Actions in Distributed Information-Rich Environments. In: Mirjana Ivanović, Costin Bădică, Jürgen Dix, Zoran Jovanović, Michele Malgeri, Miloš Savić (Ed.), Intelligent Distributed Computing XI: . Paper presented at Intelligent Distributed Computing XI (pp. 49-60). Cham: Springer, 737
Open this publication in new window or tab >>Towards a Paraconsistent Approach to Actions in Distributed Information-Rich Environments
2018 (English)In: Intelligent Distributed Computing XI / [ed] Mirjana Ivanović, Costin Bădică, Jürgen Dix, Zoran Jovanović, Michele Malgeri, Miloš Savić, Cham: Springer, 2018, Vol. 737, p. 49-60Conference paper, Published paper (Refereed)
Abstract [en]

The paper introduces ActLog, a rule-based language capable of specifying actions paraconsistently. ActLog is an extension of 4QL Bel " role="presentation"> Bel , a rule-based language for reasoning with paraconsistent and paracomplete belief bases and belief structures. Actions considered in the paper act on belief bases rather than states represented as sets of ground literals. Each belief base stores multiple world representations which can be though of as a representation of possible states. In this context ActLog’s action may be then seen as a method of transforming one belief base into another. In contrast to other approaches, ActLog permits to execute actions even if the underlying belief base state is partial or inconsistent. Finally, the framework introduced in this paper is tractable.

Place, publisher, year, edition, pages
Cham: Springer, 2018
Series
Studies in Computational Intelligence, ISSN 1860-949X, E-ISSN 1860-9503 ; 737
Keywords
Action languages; Paraconsistent reasoning; Paracomplete reasoning; Belief structures
National Category
Computer Sciences
Identifiers
urn:nbn:se:liu:diva-153430 (URN)10.1007/978-3-319-66379-1_5 (DOI)000451440400005 ()9783319663784 (ISBN)9783319663791 (ISBN)
Conference
Intelligent Distributed Computing XI
Available from: 2018-12-14 Created: 2018-12-14 Last updated: 2019-01-24
Dunin-Kęplicz, B., Powala (Strachocka), A. & Szalas, A. (2018). Variations on Jaśkowski’s Discursive Logic. In: Ángel GarridoUrszula Wybraniec-Skardowska (Ed.), The Lvov-Warsaw School. Past and Present: (pp. 485-497). Cham: Birkhäuser
Open this publication in new window or tab >>Variations on Jaśkowski’s Discursive Logic
2018 (English)In: The Lvov-Warsaw School. Past and Present / [ed] Ángel GarridoUrszula Wybraniec-Skardowska, Cham: Birkhäuser , 2018, p. 485-497Chapter in book (Refereed)
Abstract [en]

Stanisław Jaśkowski, in his 1948–1949 papers on propositional calculus for contradictory deductive systems, proposed discursive logic D2. The main motivation behind D2 is the need to properly deal with contradictions that naturally appear in many areas of philosophy and discourse. The intuitive justification of this logic reflects knowledge fusion occurring when “the theses advanced by several participants in a discourse are combined into a single system.” This point of view was seminal in the mid twentieth century and remains visionary nowadays.

In contemporary autonomous systems operating in dynamic, unpredictable information-rich environments, distributed reasoning routinely takes place. This explains the key role of knowledge fusion, among others, in Distributed Artificial Intelligence. Therefore, different types of modern knowledge and belief bases become primarily concerned with inconsistent or lacking information. This requirement leads to recent approaches to paraconsistent and paracomplete reasoning, where nonmonotonic techniques for disambiguating inconsistencies and completing missing knowledge can be applied.

In this chapter we remind Jaśkowski’s seminal, pioneering work on paraconsistent reasoning and indicate some of its relations to contemporary research on reasoning in Distributed AI.

Place, publisher, year, edition, pages
Cham: Birkhäuser, 2018
Series
Studies in Universal Logic
National Category
Computer Sciences
Identifiers
urn:nbn:se:liu:diva-153433 (URN)10.1007/978-3-319-65430-0_34 (DOI)9783319654294 (ISBN)9783319654300 (ISBN)
Available from: 2018-12-14 Created: 2018-12-14 Last updated: 2019-01-10Bibliographically approved
Doherty, P. & Szalas, A. (2016). An Entailment Procedure for Kleene Answer Set Programs. In: Sombattheera C., Stolzenburg F., Lin F., Nayak A. (Ed.), Multi-disciplinary Trends in Artificial Intelligence. MIWAI 2016.: . Paper presented at Multi-disciplinary Trends in Artificial Intelligence. MIWAI 2016. (pp. 24-37). Springer, 10053
Open this publication in new window or tab >>An Entailment Procedure for Kleene Answer Set Programs
2016 (English)In: Multi-disciplinary Trends in Artificial Intelligence. MIWAI 2016. / [ed] Sombattheera C., Stolzenburg F., Lin F., Nayak A., Springer, 2016, Vol. 10053, p. 24-37Conference paper, Published paper (Refereed)
Abstract [en]

Classical Answer Set Programming is a widely known knowledge representation framework based on the logic programming paradigm that has been extensively studied in the past decades. Semantic theories for classical answer sets are implicitly three-valued in nature, yet with few exceptions, computing classical answer sets is based on translations into classical logic and the use of SAT solving techniques. In this paper, we introduce a variation of Kleene three-valued logic with strong connectives, R3" role="presentation">R3, and then provide a sound and complete proof procedure for R3" role="presentation">R3 based on the use of signed tableaux. We then define a restriction on the syntax of R3" role="presentation">R3 to characterize Kleene ASPs. Strongly-supported models, which are a subset of R3" role="presentation">R3 models are then defined to characterize the semantics of Kleene ASPs. A filtering technique on tableaux for R3" role="presentation">R3 is then introduced which provides a sound and complete tableau-based proof technique for Kleene ASPs. We then show a translation and semantic correspondence between Classical ASPs and Kleene ASPs, where answer sets for normal classical ASPs are equivalent to strongly-supported models. This implies that the proof technique introduced can be used for classical normal ASPs as well as Kleene ASPs. The relation between non-normal classical and Kleene ASPs is also considered.

Place, publisher, year, edition, pages
Springer, 2016
Series
Lecture Notes in Computer Science, ISSN 0302-9743, E-ISSN 1611-3349 ; 10053
National Category
Computer and Information Sciences
Identifiers
urn:nbn:se:liu:diva-134767 (URN)10.1007/978-3-319-49397-8_3 (DOI)000389332100003 ()978-3-319-49396-1 (ISBN)978-3-319-49397-8 (ISBN)
Conference
Multi-disciplinary Trends in Artificial Intelligence. MIWAI 2016.
Projects
CADICSELLIITCUASSymbiCloudNFFP6
Available from: 2017-02-24 Created: 2017-02-24 Last updated: 2018-01-13
Doherty, P., Kvarnström, J. & Szalas, A. (2016). Iteratively-Supported Formulas and Strongly Supported Models for Kleene Answer Set Programs. In: Michael, Loizos; Kakas, Antonis (Ed.), Logics in Artificial Intelligence: 15th European Conference, JELIA 2016, Larnaca, Cyprus, November 9-11, 2016, Proceedings. Paper presented at 15th European Conference on Logics in Artificial Intelligence, JELIA 2016; Larnaca; Cyprus; 9 November 2016 through 11 November 2016 (pp. 536-542). Springer Publishing Company
Open this publication in new window or tab >>Iteratively-Supported Formulas and Strongly Supported Models for Kleene Answer Set Programs
2016 (English)In: Logics in Artificial Intelligence: 15th European Conference, JELIA 2016, Larnaca, Cyprus, November 9-11, 2016, Proceedings, Springer Publishing Company, 2016, p. 536-542Conference paper, Published paper (Refereed)
Abstract [en]

In this extended abstract, we discuss the use of iteratively-supported formulas (ISFs) as a basis for computing strongly-supported models for Kleene Answer Set Programs (ASPK). ASPK programs have a syntax identical to classical ASP programs. The semantics of ASPK programs is based on the use of Kleene three-valued logic and strongly-supported models. For normal ASPK programs, their strongly supported models are identical to classical answer sets using stable model semantics.  For disjunctive ASPK programs, the semantics weakens the minimality assumption resulting in a classical interpretation for disjunction. We use ISFs to characterize strongly-supported models and show that they are polynomially bounded.

Place, publisher, year, edition, pages
Springer Publishing Company, 2016
Series
Lecture Notes in Computer Science, ISSN 0302-9743, E-ISSN 1611-3349 ; 10021
National Category
Computer and Information Sciences
Identifiers
urn:nbn:se:liu:diva-134419 (URN)10.1007/978-3-319-48758-8_36 (DOI)000389316500036 ()978-3-319-48757-1 (ISBN)978-3-319-48758-8 (ISBN)
Conference
15th European Conference on Logics in Artificial Intelligence, JELIA 2016; Larnaca; Cyprus; 9 November 2016 through 11 November 2016
Projects
CADICSELLIITCUASSymbiCloudSHERPANFFP6 KISA
Available from: 2017-02-10 Created: 2017-02-10 Last updated: 2018-01-13
Dunin-Keplicz, B. & Szalas, A. (2015). A New Perspective on Goals. In: Sujata Ghosh and Jakub Szymanik (Ed.), The Facts Matter: Essays on Logic and Cognition in Honour of Rineke Verbrugge: (pp. 50-66). London: College Publications
Open this publication in new window or tab >>A New Perspective on Goals
2015 (English)In: The Facts Matter: Essays on Logic and Cognition in Honour of Rineke Verbrugge / [ed] Sujata Ghosh and Jakub Szymanik, London: College Publications, 2015, p. 50-66Chapter in book (Other academic)
Abstract [en]

This book is in celebration of Rineke Verbrugge's 50th birthday. It is a product of an incredible effort on the part of Rineke's teachers, colleagues, students and friends who have all been won over by her ever-encouraging and positive presence in academia and also in daily life. Pertaining to Rineke's research interests, the book features eight articles on a wide range of topics - from theories of arithmetic to a study on autism. The papers on hybrid logic, formal theories of belief, probability, goals, social networks, and bisimulations enrich the logic section of the book while papers on cognitive strategizing and social cognition bring up the cognitive perspective. The themes themselves provide a compelling perception of the vast expanse of Rineke's academic interests and endeavours. A series of personal comments, stories, anecdotes, and pictures constitute the latter part of the book, adding a distinct personal touch to this volume.

Place, publisher, year, edition, pages
London: College Publications, 2015
National Category
Computer and Information Sciences
Identifiers
urn:nbn:se:liu:diva-120978 (URN)978-1-84890-173-5 (ISBN)
Available from: 2015-09-01 Created: 2015-09-01 Last updated: 2018-01-11Bibliographically approved
Dunin-Keplicz, B., Strachocka, A., Szalas, A. & Verbrugge, R. (2015). Paraconsistent semantics of speech acts. Neurocomputing, 151(2), 943-952
Open this publication in new window or tab >>Paraconsistent semantics of speech acts
2015 (English)In: Neurocomputing, ISSN 0925-2312, E-ISSN 1872-8286, Vol. 151, no 2, p. 943-952Article in journal (Refereed) Published
Abstract [en]

This paper discusses an implementation of four speech acts: assert, concede, request and challenge in a paraconsistent framework. A natural four-valued model of interaction yields multiple new cognitive situations. They are analyzed in the context of communicative relations, which partially replace the concept of trust. These assumptions naturally lead to six types of situations, which often require performing conflict resolution and belief revision. The particular choice of a rule-based, DATALOC. like query language 4QL as a four-valued implementation framework ensures that, in contrast to the standard two-valued approaches, tractability of the model is achieved.

Place, publisher, year, edition, pages
Elsevier, 2015
Keywords
Paraconsistent modeling; Communication; Speech acts; Tractable models; Four-valued logic; Conflict resolution
National Category
Computer and Information Sciences
Identifiers
urn:nbn:se:liu:diva-114224 (URN)10.1016/j.neucom.2014.10.001 (DOI)000347753500045 ()
Available from: 2015-02-16 Created: 2015-02-16 Last updated: 2018-01-11
Doherty, P. & Szalas, A. (2015). Stability, Supportedness, Minimality and Kleene Answer Set Programs. In: Thomas Eiter, Hannes Strass, Mirosław Truszczynski, Stefan Woltran (Ed.), Advances in Knowledge Representation, Logic Programming, and Abstract Argumentation: Essays Dedicated to Gerhard Brewka on the Occasion of His 60th Birthday (pp. 125-140). Springer
Open this publication in new window or tab >>Stability, Supportedness, Minimality and Kleene Answer Set Programs
2015 (English)In: Advances in Knowledge Representation, Logic Programming, and Abstract Argumentation: Essays Dedicated to Gerhard Brewka on the Occasion of His 60th Birthday / [ed] Thomas Eiter, Hannes Strass, Mirosław Truszczynski, Stefan Woltran, Springer, 2015, p. 125-140Chapter in book (Refereed)
Abstract [en]

Answer Set Programming is a widely known knowledge representation framework based on the logic programming paradigm that has been extensively studied in the past decades. The semantic framework for Answer Set Programs is based on the use of stable model semantics. There are two characteristics intrinsically associated with the construction of stable models for answer set programs. Any member of an answer set is supported through facts and chains of rules and those members are in the answer set only if generated minimally in such a manner. These two characteristics, supportedness and minimality, provide the essence of stable models. Additionally, answer sets are implicitly partial and that partiality provides epistemic overtones to the interpretation of disjunctiver ules and default negation. This paper is intended to shed light on these characteristics by defining a semantic framework for answer set programming based on an extended first-order Kleene logic with weak and strong negation. Additionally, a definition of strongly supported models is introduced, separate from the minimality assumption explicit in stable models. This is used to both clarify and generate alternative semantic interpretations for answer set programs with disjunctive rules in addition to answer set programs with constraint rules. An algorithm is provided for computing supported models and comparative complexity results between strongly supported and stable model generation are provided.

Place, publisher, year, edition, pages
Springer, 2015
Series
Lecture Notes in Computer Science, ISSN 0302-9743, E-ISSN 1611-3349 ; 9060
National Category
Computer Systems
Identifiers
urn:nbn:se:liu:diva-114218 (URN)10.1007/978-3-319-14726-0_9 (DOI)978-3-319-14725-3 (ISBN)978-3-319-14726-0 (ISBN)
Projects
CADICSELLIITCUASSHERPANFFP6
Available from: 2015-02-15 Created: 2015-02-15 Last updated: 2018-01-25Bibliographically approved
Nguyen, L. A., Nguyen, T.-B. & Szalas, A. (2015). Towards richer rule languages with polynomial data complexity for the Semantic Web. Data & Knowledge Engineering, 96-97, 57-77
Open this publication in new window or tab >>Towards richer rule languages with polynomial data complexity for the Semantic Web
2015 (English)In: Data & Knowledge Engineering, ISSN 0169-023X, E-ISSN 1872-6933, Vol. 96-97, p. 57-77Article in journal (Refereed) Published
Abstract [en]

We introduce a Horn description logic called Horn-DL, which is strictly and essentially richer than Horn-Reg(1), Horn-SHTQ and Horn-SROIQ, while still has PTime data complexity. In comparison with Horn-SROIQ, Horn-DL additionally allows the universal role and assertions of the form irreflexive(s), -s(a, b), a b. More importantly, in contrast to all the well-known Horn fragments epsilon L, DL-Lite, DLP, Horn-SHIQ, and Horn-SROIQ of description logics, Horn-DL allows a form of the concept constructor "universal restriction" to appear at the left hand side of terminological inclusion axioms. Namely, a universal restriction can be used in such places in conjunction with the corresponding existential restriction. We develop the first algorithm with PTime data complexity for checking satisfiability of Horn-DL knowledge bases.

Place, publisher, year, edition, pages
ELSEVIER SCIENCE BV, 2015
Keywords
Description logics; Semantic Web; Rule-based languages; Horn fragments; Horn-DL
National Category
Computer Sciences
Identifiers
urn:nbn:se:liu:diva-120363 (URN)10.1016/j.datak.2015.04.005 (DOI)000357627200006 ()
Available from: 2015-07-31 Created: 2015-07-31 Last updated: 2018-01-11
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