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

Formalisation and logical properties of the maximal ideal recursive semantics for weighted defeasible logic programming

Possibilistic defeasible logic programming (P-DeLP) is a logic programming framework which combines features from argumentation theory and logic programming, in which defeasible rules are attached with weights expressing their relative belief or preference strength. In P-DeLP,a conclusion succeeds if there exists an argument that entails the conclusion and this argument is found to be undefeated by a warrant procedure that systematically explores the universe of arguments in order to present an exhaustive synthesis of the relevant chains of pros and cons for the given conclusion. Recently, we have proposed a new warrant recursive semantics for P-DeLP, called Recursive P-DeLP (RP-DeLP for short), based on the claim that the acceptance of an argument should imply also the acceptance of all its sub-arguments which reflect the different premises on which the argument is based. This paper explores the relationship between the exhaustive dialectical analysis-based semantics of P-DeLP and the recursive-based semantics of RP-DeLP, and analyses a non-monotonic inference operator for RP-DeLP which models the expansion of a given program by adding new weighted facts associated with warranted conclusions. Given the recursive-based semantics of RP-DeLP, we have also implemented an argumentation framework for RP-DeLP that is able to compute not only the output of warranted and blocked conclusions, but also explain the reasons behind the status of each conclusion. We have developed this framework as a stand-alone application with a simple text-based input/output interface to be able to use it as part of other artificial intelligence systemsThis research was partially supported by the Spanish projects EdeTRI (TIN2012-39348-C02-01) and AT (CONSOLIDER- INGENIO 2010, CSD2007-00022)

An algebraic approach for action based default reasoning

Often, we assume that an action is permitted simply because it is not explicitly forbidden; or, similarly, that an action is forbidden simply because it is not explicitly permitted. This kind of assumptions appear, e.g., in autonomous computing systems where decisions must be taken in the presence of an incomplete set of norms regulating a particular scenario. Combining default and deontic reasoning over actions allows us to formally reason about such assumptions. With this in mind, we propose a logical formalism for default reasoning over a deontic action logic. The novelty of our approach is twofold. First, our formalism for default reasoning deals with actions and action operators, and it is based on the deontic action logic originally proposed by Segerberg in [27]. Second, inspired by Segerberg?s approach, we use tools coming from the theory of Boolean Algebra. These tools allow us to extend Segerberg?s algebraic completeness result to the setting of Default Logics.Fil: Castro, Pablo Francisco. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Nacional de Rio Cuarto. Facultad de Cs.exactas Fisicoquímicas y Naturales. Departamento de Computación. Grupo de Ingeniería de Software; ArgentinaFil: Cassano, Valentin. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física. Sección Ciencias de la Computación; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Fervari, Raul Alberto. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física. Sección Ciencias de la Computación; ArgentinaFil: Areces, Carlos Eduardo. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física. Sección Ciencias de la Computación; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentin

Adaptive logic characterizations of input/output logic

We translate unconstrained and constrained input/output logics as introduced by Makinson and van der Torre to modal logics, using adaptive logics for the constrained case. The resulting reformulation has some additional benefits. First, we obtain a proof-theoretic (dynamic) characterization of input/output logics. Second, we demonstrate that our framework naturally gives rise to useful variants and allows to express important notions that go beyond the expressive means of input/output logics, such as violations and sanctions

Electronic institutions with normative environments for agent-based E-contracting

Tese de doutoramento. Engenharia Informática. Faculdade de Engenharia. Universidade do Porto. 201

Ideality and subideality from a computational point of view

Why should Law need automated proof systems? The answer to this question implies an answer to the following question: Is logic needed in Law? In fact it has been argued that logics are useless for Law (see, for example, Kelsen 1989). We believe that logic, and deontic logics in particular - but also modal logics - have a role to play in Law; for example if one wants to study what the relationships are among the various degrees of adjudication in Italian Law, one should note that they give rise to a transitive, irreflexive and finite structure, which is the frame of the modal logic of provability GL; one of the most important properties of such a logic is that no system, (no court) in this frame, could claim its own correctness without becoming incorrect (Boolos 1993, Smullyan 1988), but the correctness of a lower court can be established by a higher one. This example shows that the study of modal logic can help in finding certain already known properties of legal systems. Moreover, each time we are dealing with the notions of Obligation and Permission, and we are interested in the study of their mutual relationship, we can arrange them into a deontic framework, thus producing a certain kind of deontic logic. Finally a hint for the use of logic in legal reasoning is given, for example in the Italian case, by the law itself; in fact article 192, 1 comma of the "Italian code of criminal procedure" prescribes that the judges state the reasons of their adjudication; moreover several other articles of the same code, state: when evidence is valid, how evidence should be used in order to lead to an adjudication, etc. On this basis the "Italian code of criminal procedure" can be thought of as a deductive system where its articles act as the inference rules, whereas the articles of the "Italian code of criminal law" are the axioms. What does a proof system do? A proof system can work in two ways. The first of them consists of producing admissible steps one after the other according to the inference rules; in this way each step is guaranteed to be correct, but we are not led to the goal we want to prove. The other one consists of verifying whether a conclusion follows from given premises, i.e., if the adjudication follows logically from the evidence, mainly by refuting the negation of the conclusion. The system we propose is based on the logic of ideality and subideality developed by Jones and Porn, and it verifies in the above mentioned logical framework whether a given conclusion follows from given premises. Moreover, due to its basic control structure it can also be used as an analytic direct proof system

Modal tableaux for nonmonotonic reasoning

The tableau-like proof system KEM has been proven to be able to cope with a wide variety of (normal) modal logics. KEM is based on D'Agostino and Mondadori's (1994) classical proof system KE, a combination of tableau and natural deduction inference rules which allows for a restricted ("analytic") Use of the cut rule. The key feature of KEM, besides its being based neither on resolution nor on standard sequent/tableau inference techniques, is that it generates models and checks them using a label scheme to bookkeep "world" paths. This formalism can be extended to handle various system of multimodal logic devised for dealing with nonmonotonic reasoning, by relying in particular on Meyer and van der Hoek's (1992) logic for actuality and preference. In this paper we shall be concerned with developing a similar extension this time by relying on Schwind and Siegel's (1993,1994) system H, another multimodal logic devised for dealing with nonmonotonic inference