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Strategic Argumentation is NP-Complete
[article]

2013
*
arXiv
*
pre-print

For a detailed exposition see (Governatori and

arXiv:1312.4287v1
fatcat:nqkfmizmlzcinobf2clcarknvm
*Rotolo*2008) . Definition 6 (Language). ... Theorem 10 ((Governatori and*Rotolo*2008)). The Restoring Sociality Problem is NP-complete. ... In fact, we map the Restoring Sociality Problem (Governatori and*Rotolo*2008) into the Strategic Argumentation Problem. ...##
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Computing Temporal Defeasible Logic
[chapter]

2013
*
Lecture Notes in Computer Science
*

We investigate the complexity of temporal defeasible logic, and propose an efficient algorithm to compute the extension of any theory. The logic and algorithm are discussed in regard to modeling deadlines and normative retroactivity. Introduction Defeasible Logic (DL) [22, 3] is historically the first of a family of approaches based on the idea of logic programming without negation as failure. DL is a simple, efficient but flexible non-monotonic formalism capable of dealing with many different

doi:10.1007/978-3-642-39617-5_13
fatcat:qx7jtl2nmbg2rkq4hsgh5evkfa
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... ntuitions of non-monotonic reasoning. The logic was designed to be easily implementable right from the beginning, unlike most other approaches, and has a linear complexity [20] . DL proved to be modular and flexible. In particular, propositional DL has been recently extended in two different directions. In a first case, different types of modal operators (capturing notions such as directed and undirected deontic statements, actions, beliefs, and intentions) have been embedded within propositional DL [?,11]. The result was a number of logics having still linear complexity and being able to model the deliberation of cognitive agents and their interplay with normative systems. Some implementations have been recently developed for such logics [?,?,17]. DL has been also extended to capture temporal aspects of normative reasoning [15, 12] several specific phenomena, such as legal positions [15] and modifications [10, 12], deadlines [8] . Although Temporal Defeasible Logic (TDL) proved to be sufficiently expressive for those purposes, and many variants of it have been proposed accordingly, no systematic investigation on the proof-theoretic and computational properties of TDL has been so far carried out. This paper is a first step in this direction. In particular, we will present an expressive variant of TDL, which is computationally feasible. This variant is able to represent different types of deadlines and capture backward causation and normative retroactivity. We will prove that it is possible in all cases to compute the complete set of consequences of any given TDL theory in linear time, thus preserving the nice computational features of standard DL. The layout of the paper is as follows. Section 2 describes a variant of TDL. Section 3 considers a first case-study: modeling the concept of deadline. Section 4 investigates the complexity of the logic, and proposes an algorithm to compute the extension of any theory. Section 5 discusses the approach and considers a second case-study: modeling retroactivity. A section on related work ends the paper.##
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Temporal Reasoning and MAS

2011
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Social Science Research Network
*

In this paper we investigate if it is possible and useful to reason about time within social/normative multi-agent systems (MAS) by taking into account the general guidelines of tense logic. We focus on the combination of special-purpose logics: we provide a formal account in which a minimal temporalization helps in reasoning about time in an abstract way. We also explore a new variant of deontic tense logic by using a hybrid tense logic. The accounts provided allow to model temporal provisions

doi:10.2139/ssrn.1785412
fatcat:n4kj2gdti5chdms7vvljcujtqm
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... within both particular norms and general legal principles, and also help in the detection of breaches of good faith and confidence.##
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Norm Compliance in Business Process Modeling
[chapter]

2010
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Lecture Notes in Computer Science
*

We investigate the concept of norm compliance in business process modeling. In particular we propose an extension of Formal Contract Logic (FCL), a combination of defeasible logic and a logic of violation, with a richer deontic language capable of capture many different facets of normative requirements. The resulting logic, called Process Compliance Logic (PCL), is able to capture both semantic compliance and structural compliance. This paper focuses on structural compliance, that is we show

doi:10.1007/978-3-642-16289-3_17
fatcat:pxlo3uclzjaqxcbqzxcoa2p5s4
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... PCL can capture obligations concerning the structure of a business process.##
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Defeasible Logic: Agency, Intention and Obligation
[chapter]

2004
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Lecture Notes in Computer Science
*

We propose a computationally oriented non-monotonic multi-modal logic arising from the combination of agency, intention and obligation. We argue about the defeasible nature of these notions and then we show how to represent and reason with them in the setting of defeasible logic. Introduction This paper combine two perspectives: (a) a cognitive account of agents that specifies motivational attitudes; (b) modelling societies of agents by means of normative concepts [4] . For the first approach,

doi:10.1007/978-3-540-25927-5_8
fatcat:jgpm4ugtj5djnkoe42tv5fc5oi
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... ur background is the belief-desire-intention (BDI) architecture, where mental attitudes are taken as primitives to give rise to a set of Intentional Agent Systems [23, 2] . This view has been proved to be interesting especially when the behaviour of agents is the outcome of a rational balance among their (possibly conflicting) mental states [3, 24] . The normative aspect is based on some intuitions about agents and their societies, in which it is assumed that normative concepts play a decisive role, allowing for the co-ordination of autonomous agents [22, 10, 12] . Our approach has in general several points of contact with the BOID architecture [4, 5, 8, 6] , where a number of strategies are provided for solving conflicts among informational and motivational attitudes. BOID provides logical criteria (i) to retract agent's attitudes with the changing environment, and so (ii) to settle conflicts by stating different general policies corresponding to the agent type considered. A realistic agent thus corresponds to a conflict-resolution type in which beliefs override all other factors, while other agent types, such as simple-minded, selfish or social ones adopt different orders of overruling. As in the BOID architecture, our system is rule-based. In particular, it is developed in the setting of Defeasible Logic. All components are represented as defeasible conditionals. A rule such as p ⇒ K q means that, given p, this implies defeasibly agent's belief that q. Our approach adopts a slightly different perspective. Our claim is to We develop a constructive account of BDI multi-modal logics where the rules are meant to devise suitable logical conditions for introducing modalities. If so, rules may also contain modalised literals, as for example in I p ⇒ K q, where I is a BDI operator of intention. In the same spirit, possible conversions of a modality into another can be accepted, as when the applicability of I p ⇒ K q may permit to obtain Iq. Based on this intuitions, our focus will be on Bratman's [3] concept of policy-based intention [11] . The relation between mental attitudes and non-monotonicity should not sound surprising. Recent works by Thomason [27] and on BOID confirm this trend. Such a connection, with regard to epistemic logics, has already received much attention in the AI community [19] . However, the notion of defeasibility may play a new role A. Lomuscio and D. Nute (eds)##
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Semantics for Modelling Reason-Based Preferences
[chapter]

2015
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Lecture Notes in Computer Science
*

*Antonino*

*Rotolo*was supported by the Unibo FARB 2012 project Mortality Salience, Legal and Social Compliance, and Economic Behaviour: Theoretical Models and Experimental Methods. ...

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Computing Private International Law
[chapter]

2021
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Frontiers in Artificial Intelligence and Applications
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This paper develops a new comprehensive computational framework for reasoning about private international law that encompasses the reasoning patterns modeled by previous works [3,8,9]. The framework is a multi-modal extension of [10] preserving some nice properties of the original system, including some efficient algorithms to compute the extensions of normative theories representing legal systems.

doi:10.3233/faia210334
fatcat:lmauxvkcxrcfbhm6br4tnsnvh4
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Logics for Legal Dynamics
[chapter]

2015
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Logic in the Theory and Practice of Lawmaking
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most cases to instances of the notion of norm defeasibility [Governatori and

doi:10.1007/978-3-319-19575-9_12
fatcat:oko3zyfde5dqfkovfo5vzijls4
*Rotolo*, 2010] . ... Some works (see, in particular, [Governatori and*Rotolo*, 2010] ) have attempted to address these research issues. ...##
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A computational framework for institutional agency

2008
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Artificial Intelligence and Law
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This paper provides a computational framework, based on Defeasible Logic, to capture some aspects of institutional agency. Our background is Kanger-Lindahl-Pörn account of organised interaction, which describes this interaction within a multi-modal logical setting. This work focuses in particular on the notions of counts-as link and on those of attempt and of personal and direct action to realise states of affairs. We show how standard Defeasible Logic can be extended to represent these

doi:10.1007/s10506-007-9056-y
fatcat:iimydlwmhndpfdzy2xtowea4cu
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... : the resulting system preserves some basic properties commonly attributed to them. In addition, the framework enjoys nice computational properties, as it turns out that the extension of any theory can be computed in time linear to the size of the theory itself.##
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Free Choice Permission in Defeasible Deontic Logic
[chapter]

2020
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Frontiers in Artificial Intelligence and Applications
*

*Rotolo*/ Free Choice Permission in Defeasible Deontic Logic ...

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Heuristics in Argumentation: A Game-Theoretical Investigation

2008
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Social Science Research Network
*

EUI WP LAW 2008/31 ©2008 Régis Riveret, Henry Prakken,

doi:10.2139/ssrn.1317349
fatcat:j42argapdrfxnkbgspfrvjvpim
*Antonino**Rotolo*, Giovanni Sartor Régis Riveret, Henry Prakken,*Antonino**Rotolo*, Giovanni Sartor In any case, this assumption is reasonable ...*Rotolo*, Giovanni Sartor ...##
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A Preference-Based Semantics for CTD Reasoning
[chapter]

2014
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Lecture Notes in Computer Science
*

*Antonino*

*Rotolo*was supported by the Unibo FARB 2012 project Mortality Salience, Legal and Social Compliance, and Economic Behaviour: Theoretical Models and Experimental Methods. ...

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Rule-Based Agents in Temporalised Defeasible Logic
[chapter]

2006
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Lecture Notes in Computer Science
*

This paper provides a framework based on temporal defeasible logic to reason about deliberative rule-based cognitive agents. Compared to previous works in this area our framework has the advantage that it can reason about temporal rules. We show that for rule-based cognitive agents deliberation is more than just deriving conclusions in terms of their mental components. Our paper is an extension of [5, 6] in the area of cognitive agent programming.

doi:10.1007/978-3-540-36668-3_6
fatcat:k7ngkr4qrfaoxdiudhnj4eag4m
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Possible World Semantics for Defeasible Deontic Logic
[chapter]

2012
*
Lecture Notes in Computer Science
*

Defeasible Deontic Logic is a simple and computationally efficient approach for the representation of normative reasoning. Traditionally defeasible logics are defined proof theoretically based on the proof conditions for the logic. While several logic programming, operational and argumentation semantics have been provided for defeasible logics, possible world semantics for (modal) defeasible logics remained elusive. In this paper we address this issue. (Defeasible Multi-modal Logic), based on

doi:10.1007/978-3-642-31570-1_4
fatcat:eixxckbqtngkxhqshc3gwkjewu
## more »

... , which covers all existing variants of Defeasible Deontic Logic. Section 4 discusses how to interpret Defeasible Multi-modal Logic in neighbourhood semantics and identifies one open problem. 2 Defeasible Deontic Logic: An Informal Presentation DL has three basic kinds of features: facts, rules, and a superiority relation among rules. Facts are indisputable statements. Rules are usually of three types: strict rules, marked by the arrow →, correspond to the monotonic part of the logic and support indisputable conclusions whenever their antecedents, too, are indisputable 3 . Defeasible rules, marked by ⇒, can be defeated by contrary evidence. Defeaters, marked by Y, cannot lead to any conclusion but are used to defeat some defeasible rules by producing evidence to the contrary. The superiority relation (>) provides information about the relative strength of rules, i.e., about which rules can overrule which other rules. Defeasible Deontic Logic is a family of logics that extend DL by adding deontic and other modal operators. The purpose is to study the interplay between deontic concepts (such as obligations and permission) and other modal components such as counts-as concepts and agents' actions [15] , or agents' beliefs and intentions [14] . The resulting extended language is based on a family of different rules, where each type is labeled by a different modal operator P i : the idea is that each rule, if parametrized by P i , it is meant to govern the derivation of formulas modalized with P i . The approach we have elsewhere developed in Defeasible Deontic Logic is thus twofold. First, we take a constructive interpretation of any modal operator P i : if we can build a derivation of p using rules for P i , then we also have a derivation of P i p. Second, derivability in classical logic is replaced with a practical and feasible notion like derivability in DL. Thus the intuition is that we are allowed to derive P i p if we can prove p with the mode P i in DL. For example, a rule like p 1 , . . . , p n ⇒ OBL q means that, if p 1 , . . . , p n are the case or proved, then the logical machinery allows us to derive q with mode OBL, and so OBLq. In general, for any P i Γ Γ ⇒ 2 i q Γ | ∼ P i q Defeasible Deontic Logic defines some interaction patterns between modalities: in particular, one permits to use rules for a modality P i as they were for another modality P j (rule conversions), and one considers conflicts between rules. Rule Conversions The notion of rule conversion allows us to model peculiar interactions between different modal operators (for an extensive conceptual discussion, see [14] ). To give an example, suppose we have that a ⇒ BEL b and that we derive a using a rule labeled by INT. Can we conclude INTb? If the answer is positive, conversions can be represented as follows: For the sake of simplicity, we will not consider those rules in the logics discussed in this paper.##
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Labelled proofs for quantified modal logic
[chapter]

1996
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Lecture Notes in Computer Science
*

In this paper we describe a modal proof system arising from the combination of a tableau-like classical system, which incorporates a restricted ("analytic") version of the cut rule, with a label formalism which allows for a specialised, logic-dependent unification algorithm. The system provides a uniform proof-theoretical treatment of first-order (normal) modal logics with and without the Barcan Formula and/or its converse.

doi:10.1007/3-540-61630-6_5
fatcat:y4taichtfzbvvhnlmbcdyhedcq
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