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...erminates and its computational complexity is O(|R |∗ |HB|). Proof Sketch. Termination is ensured since at every iteration either no modification occurs and line 36 ends the computation, or a literal is removed from HB. This set is finite, since the sets of facts and rules are finite, thus the process eventually empties HB. This bounds also the complexity to the number of rules and literals in HB, since each modal literal is processed once, and every time we scan the set of rules. Theorem 2. Algorithm 1 DEFEASIBLEEXTENSION is sound and complete. Proof Omissis. A similar result can be found in [21]. 4 Conclusions and Related Work This article provides a fresh characterisation for motivational states as the concepts of desire, goal, intention, and social intention obtained through a deliberative process based on various types of preferences among desired outcomes. In this sense, this contribution has strong connections with [5,6,7] but presents significant improvements in at least two respects. First, while in those works the agent deliberation is simply the result of the derivation of mental states from precisely the corresponding rules of the logic, here the proof theory is much more a...

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...r several applied domains, such as in business process modeling [13], normative multi-agent systems [14], temporal deontic reasoning [15], and reasoning about different types of defeasible permission =-=[16]-=-. Nevertheless, no semantic model-theoretic analysis of the operator ⊗ has been so far provided. In this paper we fill the gap and define a suitable possible-world semantics for this operator. Such se...

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...permissive norms. – If P 6= ∅, then PosPerm(N,Φ) = {ψ ∈ LP : ψ ∈ out(O ∪ {(φ′, ψ′)}, Φ), for some (φ′, ψ′) ∈ P}}. – If P = ∅, then PosPerm(N,Φ) = out(O,Φ). Intuitively, permissive norms are treated like weak obligatory norms, the basic difference is that while the latter may be used jointly, the former may only be applied one by one. As an illustration of such difference, image a situation in which a man is permitted to date either one of two girls, but not both of them. Alternative definitions of positive permission can be found in Makinson and van der Torre [22], Stolpe [29] and Governatori [14]. 2.4 Complexity theory Complexity theory is the theory to investigate the time, memory, or other resources required for solving computational problems. In this subsection we briefly review those concepts and results from complexity theory which will be used in this paper. More comprehensive introduction of complexity theory can be found in [3] We assume the readers are familiar with notions like Turing machine and the complexity class P, NP and coNP. Oracle Turing machine and two complexity classes related to oracle Turing machine will be used in this paper. Definition 5 (oracle Turing machin...

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...valuation of two or more logical operators (e.g., modal operators or quantifiers). Section 2 presents some example. Hobbs’s logic, by avoiding embeddings of operators within the scope of other operators, straightforwardly and uniformly handles these readings, that are intrinsically prevented in many traditional logical frameworks for Natural Language Semantics. 2 Related work Some previous approaches try to model, in some deontic settings, sentences coming from existing norms. The most representative work is perhaps [30]. Examples of real norms formalized in deontic logic may be also found in [11] and [1]. Many current state-of-the-art approaches try to formalize legal knowledge via Event Calculus [16] [22]. Event Calculus is a neo-Davidsonian logical language that extends the original account of Reification (see [10] for a discussion). A recent approach in the line is [12]. In [12], it is argued that Event Calculus predicates for handling time cannot be directly used for handling also deontic meaning. Therefore, a new version is proposed to incorporate the deontic effect of norms, so that they can be used for compliance checking. Similar proposals are [24], [7], and [8]. However, [12]...

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... conclude. For permission, we have the same conditions, but where we use [P]p instead of [O]p; also, we conclude [P]p if we can conclude [O]p. For the full presentation of the logic we refer to [18], =-=[21]-=-. Finally, FCL is agnostic about the nature of the literals it uses. ey can represent tasks (activities executed in a process), or propositions representing state variables and the happening of event...

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...atory [19]. The second type of permissions is just one way for modeling explicit permissive clauses for proving Pq (strong permissions of q): for an extensive treatment of defeasible permissions, see =-=[6]-=-. This reading suggests that permissions are essentially defeasible. Permission, version I (Weak Permission) +∂Plc : If P(n+1) = +∂Plc q then (1) −∆Olc∼q ∈ P(1..n). The first type of permission might ...

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...atory [19]. The second type of permissions is just one way for modeling explicit permissive clauses for proving Pq (strong permissions of q): for an extensive treatment of defeasible permissions, see =-=[8]-=-. This reading suggests that permissions are essentially defeasible. Let us only consider the positive cases: Permission, version I (Weak Permission) +∂Pl : If P(n+1) = +∂Pl q then (1) −∆Ol∼q ∈ P(1..n...

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...he applicability of obligations and prohibitions, as already has been studied by Stolpe [23] where the semantics is defined using AGM belief revision [1], Input/Output logic [19] and Defeasible Logic =-=[8]-=-. Conflict detection involving permission has already been studied by Hansen [13], however we plan to study it in a dynamic setting as future work.Acknowledgements NICTA is funded by the Australian G...