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### Applications of Linear Defeasible Logic: combining resource consumption and exceptions to energy management and business processes

Linear Logic and Defeasible Logic have been adopted to formalise different features of knowledge representation: consumption of resources, and non monotonic reasoning in particular to represent exceptions. Recently, a framework to combine sub-structural features, corresponding to the consumption of resources, with defeasibility aspects to handle potentially conflicting information, has been discussed in literature, by some of the authors. Two applications emerged that are very relevant: energy management and business process management. We illustrate a set of guide lines to determine how to apply linear defeasible logic to those contexts.

### Is Free Choice Permission Admissible in Classical Deontic Logic?

A significant part of the literature in deontic logic revolves around the discussions of puzzles and paradoxes which show that certain logical systems are not acceptable--typically, this happens with deontic KD, i.e., Standard Deontic Logic (SDL)--or which suggest that obligations and permissions should enjoy some desirable properties. One well-known puzzle is the the so-called Free Choice Permission paradox, which was originated by the following remark by von Wright in [23, p. 21]: "On an ordinary understanding of the phrase'it is permitted that', the formula'P(p q)' seems to entail'Pp Pq'. If I say to somebody'you may work or relax' I normally mean that the person addressed has my permission to work and also my permission to relax. It is up to him to choose between the two alternatives." Usually, this intuition is formalised by the following schema: P(p q) (Pp Pq) (FCP) Many problems have been discussed in the literature around FCP: for a comprehensive overview, discussion, and some solutions, see [11, 14, 20]. Three basic difficulties can be identified, among the others [11, p. 43]: - Problem 1: Permission Explosion Problem - "That if anything is permissible, then everything is, and thus it would also be a theorem that nothing is obligatory," [20], for example "If you may order a soup, then it is not true that you ought to pay the bill" [6];

### Resource-driven Substructural Defeasible Logic

Linear Logic and Defeasible Logic have been adopted to formalise different features relevant to agents: consumption of resources, and reasoning with exceptions. We propose a framework to combine sub-structural features, corresponding to the consumption of resources, with defeasibility aspects, and we discuss the design choices for the framework.

### A Labelling Framework for Probabilistic Argumentation

The combination of argumentation and probability paves the way to new accounts of qualitative and quantitative uncertainty, thereby offering new theoretical and applicative opportunities. Due to a variety of interests, probabilistic argumentation is approached in the literature with different frameworks, pertaining to structured and abstract argumentation, and with respect to diverse types of uncertainty, in particular the uncertainty on the credibility of the premises, the uncertainty about which arguments to consider, and the uncertainty on the acceptance status of arguments or statements. Towards a general framework for probabilistic argumentation, we investigate a labelling-oriented framework encompassing a basic setting for rule-based argumentation and its (semi-) abstract account, along with diverse types of uncertainty. Our framework provides a systematic treatment of various kinds of uncertainty and of their relationships and allows us to retrieve (by derivation) multiple statements (sometimes assumed) or results from the literature.

### On the Justification of Statements in Argumentation-based Reasoning

In the study of argumentation-based reasoning, argument justification has received far more attention than statement justification, often treated as a simple byproduct of the former. As a consequence, counterintuitive results and significant losses of sensitivity can be identified in the treatment of statement justification by otherwise appealing formalisms. To overcome this limitation, we propose to reappraise statement justification as a formalism-independent component. To this purpose, we introduce a novel general model of argumentation-based reasoning based on multiple levels of labellings, one of which is devoted to statement justification. This model is able to encompass several literature proposals as special cases: we illustrate this ability for the case of the ASPIC+ formalism and provide a first example of tunable statement justification in this context.

### Baroni

In the study of argumentation-based reasoning, argument justification has received far more attention than statement justification, often treated as a simple byproduct of the former. As a consequence, counterintuitive results and significant losses of sensitivity can be identified in the treatment of statement justification by otherwise appealing formalisms. To overcome this limitation, we propose to reappraise statement justification as a formalism-independent component. To this purpose, we introduce a novel general model of argumentation-based reasoning based on multiple levels of labellings, one of which is devoted to statement justification. This model is able to encompass several literature proposals as special cases: we illustrate this ability for the case of the ASPIC formalism and provide a first example of tunable statement justification in this context.

### The Rationale behind the Concept of Goal

The paper proposes a fresh look at the concept of goal and advances that motivational attitudes like desire, goal and intention are just facets of the broader notion of (acceptable) outcome. We propose to encode the preferences of an agent as sequences of "alternative acceptable outcomes". We then study how the agent's beliefs and norms can be used to filter the mental attitudes out of the sequences of alternative acceptable outcomes. Finally, we formalise such intuitions in a novel Modal Defeasible Logic and we prove that the resulting formalisation is computationally feasible.

### Thou Shalt is not You Will

The aim of this note is to discuss the reasons why temporal logic, specifically Linear Temporal Logic [7] might not be suitable to check whether the specifications of a system comply with a set of normative requirements. The debate whether it is possible to use temporal logic for the representation of norms is not a novel one (see for example [9]), and while the argument had settled for a while, the past decade saw a resurgence of the topic with many works in the fields of normative multi-agents and business process compliance advocating temporal logic as the formalism to express normative constraints on agent behaviours and process executions.

### Computing Strong and Weak Permissions in Defeasible Logic

In this paper we propose an extension of Defeasible Logic to represent and compute three concepts of defeasible permission. In particular, we discuss different types of explicit permissive norms that work as exceptions to opposite obligations. Moreover, we show how strong permissions can be represented both with, and without introducing a new consequence relation for inferring conclusions from explicit permissive norms. Finally, we illustrate how a preference operator applicable to contrary-to-duty obligations can be combined with a new operator representing ordered sequences of strong permissions which derogate from prohibitions. The logical system is studied from a computational standpoint and is shown to have liner computational complexity.

### Revision of Defeasible Logic Preferences

There are several contexts of non-monotonic reasoning where a priority between rules is established whose purpose is preventing conflicts. One formalism that has been widely employed for non-monotonic reasoning is the sceptical one known as Defeasible Logic. In Defeasible Logic the tool used for conflict resolution is a preference relation between rules, that establishes the priority among them. In this paper we investigate how to modify such a preference relation in a defeasible logic theory in order to change the conclusions of the theory itself. We argue that the approach we adopt is applicable to legal reasoning where users, in general, cannot change facts or rules, but can propose their preferences about the relative strength of the rules. We provide a comprehensive study of the possible combinatorial cases and we identify and analyse the cases where the revision process is successful. After this analysis, we identify three revision/update operators and study them against the AGM postulates for belief revision operators, to discover that only a part of these postulates are satisfied by the three operators.