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In Gärdenfors and Makinson (Artif Intell 65(2):197–245, 1994) and Gärdenfors (Knowledge representation and reasoning under uncertainty, Springer-Verlag, 1992) it was shown that it is possible to model nonmonotonic inference using a classical consequence relation plus an expectation-based ordering of formulas. In this article, we argue that this framework can be significantly enriched by adopting a conceptual spaces-based analysis of the role of expectations in reasoning. In particular, we show that this can solve various epistemological issues that surround nonmonotonic and default logics. We propose some formal criteria for constructing and updating expectation orderings based on conceptual spaces, and we explain how to apply them to nonmonotonic reasoning about objects and properties.

With the characteristics of the nonmonotonic logic and defeasible inference, abductive reasoning has been formalized in the field of artificial intelligence, dealing with the local pragmatics (e.g., the resolution of coreference, resolving syntactic and lexical ambiguity and interpreting metonymy and metaphor), recognizing discourse structure and even the speaker’s plan and other issues for natural language understanding. However, Hobbs’ analysis of abduction in recognizing the speaker’s plan was conducted only from the point of view of the verbal information processing that the listener does. To demonstrate the collaborative way that conversational partners working together to understand the logic of human acts and their intentions, this article analyzes the two conversations about the parents questioning their children’s intention for their acts with an abductive reasoning method. The results show that children and parents co-construct segments of discourse with coherence relations across several conversational turns, by that way they build together a simplified framework for understanding the logic of human acts and their intention. For example, when the father and his children co-constructed coherent segments of discourse with the result relation between them, they completed the particular intention understanding at the same time. This research helps in enriching the logic structure of artificial intelligence applications such as visual question answering models and enhancing their reasoning abilities.

Conditionals are defeasible rules of the form If A then usually B, and they play a central role in many approaches to nonmonotonic reasoning. Normal forms of conditional knowledge bases consisting of a set of such conditionals are useful to create, process, and compare the knowledge represented by them. In this article, we propose several new normal forms for conditional knowledge bases. Compared to the previously introduced antecedent normal form, the reduced antecedent normal form (RANF) represents conditional knowledge with significantly fewer conditionals by taking nonmonotonic entailments licenced by system P into account. The renaming normal form(ρNF) addresses equivalences among conditional knowledge bases induced by renamings of the underlying signature. Combining the concept of renaming normal form with other normal forms yields the renaming antecedent normal form (ρ ANF) and the renaming reduced antecedent normal form (ρ RANF). For all newly introduced normal forms, we show their key properties regarding, existence, uniqueness, model equivalence, and inferential equivalence, and we develop algorithms transforming every conditional knowledge base into an equivalent knowledge base being in the respective normal form. For the most succinct normal form, the ρ RANF, we present an algorithm KBρra systematically generating knowledge bases over a given signature in ρ RANF. We show that the generated knowledge bases are consistent, pairwise not antecedentwise equivalent, and pairwise not equivalent under signature renaming. Furthermore, the algorithm is complete in the sense that, when taking signature renamings and model equivalence into account, every consistent knowledge base is generated. Observing that normalizing the set of all knowledge bases over a signature Σ to ρ RANF yields exactly the same result as KBρra (Σ), highlights the interrelationship between normal form transformations on the one hand and systematically generating knowledge bases in normal form on the other hand.

The study of computational models for argumentation is a vibrant area of artificial intelligence and, in particular, knowledge representation and reasoning research. Arguments most often have an intrinsic structure made explicit through derivations from more basic structures. Computational models for structured argumentation enable making the internal structure of arguments explicit. Assumption-based argumentation (ABA) is a central structured formalism for argumentation in AI. In this article, we make both algorithmic and complexity-theoretic advances in the study of ABA. In terms of algorithms, we propose a new approach to reasoning in a commonly studied fragment of ABA (namely the logic programming fragment) with and without preferences. While previous approaches to reasoning over ABA frameworks apply either specialized algorithms or translate ABA reasoning to reasoning over abstract argumentation frameworks, we develop a direct declarative approach to ABA reasoning by encoding ABA reasoning tasks in answer set programming. We show via an extensive empirical evaluation that our approach significantly improves on the empirical performance of current ABA reasoning systems. In terms of computational complexity, while the complexity of reasoning over ABA frameworks is well-understood, the complexity of reasoning in the ABA+ formalism integrating preferences into ABA is currently not fully established. Towards bridging this gap, our results suggest that the integration of preferential information into ABA via so-called reverse attacks results in increased problem complexity for several central argumentation semantics.

For as long as there have been theories about common knowledge, they have been exposed to a certain amount of skepticism. Recent more sophisticated arguments question whether agents can acquire common attitudes and whether they are needed in social reasoning. I argue that this skepticism arises from assumptions about practical reasoning that, considered in themselves, are at worst implausible and at best controversial. A proper approach to the acquisition of attitudes and their deployment in decision making leaves room for common attitudes. Postulating them is no worse off than similar idealizations that are usefully made in logic and economics.

We present a general logical framework for reasoning about agents' cognitive attitudes of both epistemic type and motivational type. We show that it allows us to express a variety of relevant concepts for qualitative decision theory including the concepts of knowledge, belief, strong belief, conditional belief, desire, conditional desire, strong desire and preference. We also present two extensions of the logic, one by the notion of choice and the other by dynamic operators for belief change and desire change, and we apply the former to the analysis of single-stage games under incomplete information. We provide sound and complete axiomatizations for the basic logic and for its two extensions. The paper is under consideration in Theory and Practice of Logic Programming (TPLP)., Under consideration in Theory and Practice of Logic Programming (TPLP)

The viewer’s processes of inference making in the cinema involve the framing of hypotheses about the world of the narrative that may be overturned by subsequent information and are, therefore, nonmonotonic. The goal of narrative researchers is to understand the nature of those processes and how texts organise the deployment of those processes in order to present a narrative successfully. To do this we need methods capable of describing processes of hypothesis framing and belief revision. In this paper, I describe the application of the Transferable Belief Model to a hypothetical example of narrative comprehension based on an episode of CSI: Crime Scene Investigation as one such method.

Paraconsistent logics constitute an important class of formalisms dealing with non-trivial reasoning from inconsistent premisses. In this paper, we introduce uniform axiomatisations for a family of nonmonotonic paraconsistent logics based on minimal inconsistency in terms of sequent-type proof systems. The latter are prominent and widely-used forms of calculi well-suited for analysing proof search. In particular, we provide sequent-type calculi for Priest's three-valued minimally inconsistent logic of paradox, and for four-valued paraconsistent inference relations due to Arieli and Avron. Our calculi follow the sequent method first introduced in the context of nonmonotonic reasoning by Bonatti and Olivetti, whose distinguishing feature is the use of a so-called rejection calculus for axiomatising invalid formulas. In fact, we present a general method to obtain sequent systems for any many-valued logic based on minimal inconsistency, yielding the calculi for the logics of Priest and of Arieli and Avron as special instances., In Proceedings ICLP 2020, arXiv:2009.09158

The principle of tolerance characteristic of vague predicates is sometimes presented as a soft rule, namely as a default which we can use in ordinary reasoning, but which requires care in order to avoid paradoxes. We focus on two ways in which the tolerance principle can be modeled in that spirit, using special consequence relations. The first approach relates tolerant reasoning to nontransitive reasoning; the second relates tolerant reasoning to nonmonotonic reasoning. We compare the two approaches and examine three specific consequence relations in relation to those, which we call: strict-to-tolerant entailment, pragmatic-to-tolerant entailment, and pragmatic-to-pragmatic entailment. The first two are nontransitive, whereas the latter two are nonmonotonic.

Penalty logic is a non-classical non-monotonic logic which allows us to demonstrate the power of belief, the level of truth or the reliability of data that we are using. This logic can be useful to model human reasoning or to replace the penalty function in the sphere of Machine Learning. We can also talk about paraconsistency of this logic and suggest the definition of contradiction without negation.

The high rate of false positive alerts generated by the intrusion detection system (IDS), raises a crucial problem in the face of the security operator to differentiate between true attacks and failed ones. In order to solve this problem, several approaches have been developed relying on contextual information such as applications, services, network location, and vulnerabilities. The change of the context can be an effective factor to reduce false positive rate. However, most approaches in the literature have not dealt with this factor. Therefore, the authors propose non-monotonic ontology contextual-based approach (NOC-IDS), which represents a set of helpful contextual information in flexible format and dynamic reasoning. NOC-IDS aims in general to filter false positive alerts and to figure out relevant alerts, and helping the security operator to analyse relevant ones. NOC-IDS is defined by the description logic J C l a s s i c δ ϵ that provides non-monotonic reasoning. They illustrate the effectiveness and the powerfulness of the authors’ approach using the well-known DARPA 2000 data set.

Pavel Florensky (1882–1937), a Russian theologian, philosopher, and mathematician, argued that the religious discourse is essentially contradictory and put forward the idea of the logical theory of antinomies. Recently his views raised interesting discussions among logicians who consider him a forerunner of many non-classical logics. In this paper I discuss four interpretations of Florensky’s views: paraconsistent, L-contradictory, non-monotonic and rhetorical. In conclusion I argue for the integral interpretation which unites these four approaches.

Description Logics (DLs) under Rational Closure (RC) is a well-known framework for non-monotonic reasoning in DLs. In this paper, we address the concept subsumption decision problem under RC for nominal safe E L O ⊥ , a notable and practically important DL representative of the OWL 2 profile OWL 2 EL. Our contribution here is to define a polynomial time subsumption procedure for nominal safe E L O ⊥ under RC that relies entirely on a series of classical, monotonic E L ⊥ subsumption tests. Therefore, any existing classical monotonic E L ⊥ reasoner can be used as a black box to implement our method. We then also adapt the method to one of the known extensions of RC for DLs, namely Defeasible Inheritance-based DLs without losing the computational tractability.

We introduce a logic for knowledge representation and reasoning on protein-protein interactions. Modulo a theory, formulas describe protein structures and dynamic changes. They can be composed in order to add or remove static and dynamic observations. A second-order circumscription operator then enables nonmonotonic reasoning on the changes implied by a formula. We introduce deduction rules that produce formulas which are, up to equivalence, in a first-order fragment with decidable satisfiability and validity. Importantly, the rules can produce circumscribed formulas., Comment: In Proceedings ICLP 2019, arXiv:1909.07646

Magic sets are a Datalog to Datalog rewriting technique to optimize query answering. The rewritten program focuses on a portion of the stable model(s) of the input program which is sufficient to answer the given query. However, the rewriting may introduce new recursive definitions, which can involve even negation and aggregations, and may slow down program evaluation. This paper enhances the magic set technique by preventing the creation of (new) recursive definitions in the rewritten program. It turns out that the new version of magic sets is closed for Datalog programs with stratified negation and aggregations, which is very convenient to obtain efficient computation of the stable model of the rewritten program. Moreover, the rewritten program is further optimized by the elimination of subsumed rules and by the efficient handling of the cases where binding propagation is lost. The research was stimulated by a challenge on the exploitation of Datalog/\textsc{dlv} for efficient reasoning on large ontologies. All proposed techniques have been hence implemented in the \textsc{dlv} system, and tested for ontological reasoning, confirming their effectiveness. Under consideration for publication in Theory and Practice of Logic Programming., Comment: Paper presented at the 35th International Conference on Logic Programming (ICLP 2019), Las Cruces, New Mexico, USA, 20-25 September 2019, 16 pages

Rational closure is one of the most extensively studied nonmonotonic extensions of description logics. Nonetheless, so far it has been investigated only for description logics that satisfy the disjoint model union property, or limited fragments that support nominals. In this paper we show that for sufficiently expressive description logics, the traditional correspondence between rational closure and ranked interpretations does not hold. Therefore, in order to extend rational closure to a wider class of description logics it is necessary to change the definition of rational closure, or alternatively abandon its standard semantics. Here we pursue the former approach, and introduce stable rational closure, based on stable rankings. The resulting nonmonotonic logic is a natural extension of the standard rational closure: First, its refined exceptionality criterion yields a closure that satisfies the KLM postulates. Second, when a knowledge base enjoys the disjoint model union property, then stable rational closure equals the old notion. In the other cases, stable rankings may raise the exceptionality level of some concepts. Stable rational closure has a model-theoretic semantics based on upward-closed models, that relax the canonical models adopted in the past, in order to deal with logics that do not satisfy the disjoint union model property. Unfortunately, stable rankings do not always exist, and are not necessarily unique. However, they can be effectively enumerated for all defeasible knowledge bases in SROIQ , using any algorithm for reasoning with ranked models.

In this paper we present a duality between nonmonotonic consequence relations and well-founded convex geometries. On one side of the duality we consider nonmonotonic consequence relations satisfying the axioms of an infinitary variant of System P, which is one of the most studied axiomatic systems for nonmonotonic reasoning, conditional logic and belief revision. On the other side of the duality we consider well-founded convex geometries, which are infinite convex geometries that generalize well-founded posets. Since there is a close correspondence between nonmonotonic consequence relations and path independent choice functions one can view our duality as an extension of an existing duality between path independent choice functions and convex geometries that has been developed independently by Koshevoy and by Johnson and Dean.

We introduce a nonmonotonic procedure for preferential Description Logics in order to reason about typicality by taking probabilities of exceptions into account. We consider an extension, called ALC + T R P , of the logic of typicality ALC + T R by inclusions of the form T ( C ) ⊑ p D with probability p, whose intuitive meaning is that “all the typical Cs are Ds, and the probability that a C is not a D is 1 − p ”. We consider a notion of extension of an ABox containing only some typicality assertions, then we equip each extension with a probability. We then restrict entailment of a query F to those extensions whose probabilities belong to a given and fixed range. We propose a decision procedure for reasoning in ALC + T R P and we exploit it to show that entailment is ExpTime -complete as for the underlying ALC .

InfOCF-Web provides implementations of system P and system Z inference, and of inference relations based on c-representation with respect to various inference modes and different classes of minimal models. It has an easy-to-use online interface for computing ranking models of a conditional knowledge R, and for answering queries and comparing inference results of nonmonotonic inference relations induced by R.

The exact relationship between formal argumentation and nonmonotonic logics is a research topic that keeps on eluding researchers despite recent intensified efforts. We contribute to a deeper understanding of this relation by investigating characterizations of abstract dialectical frameworks in conditional logics for nonmonotonic reasoning. We first show that in general, there is a gap between argumentation and conditional semantics when applying several intuitive translations, but then prove that this gap can be closed when focusing on specific classes of translations., Annals of mathematics and artificial intelligence;Bd 89. 2021, H. 10/11, S. 1075-1099

This article presents results from a simulation-based study of inheritance inference, that is, inference from the typicality of a property among a "base" class to its typicality among a subclass of the class. The study aims to ascertain which kinds of inheritance inferences are reliable, with attention to the dependence of their reliability upon the type of environment in which inferences are made. For example, the study addresses whether inheritance inference is reliable in the case of "exceptional subclasses" (i.e., subclasses that are known to be atypical in some respect) and attends to variations in reliability that result from variations in the entropy level of the environment. A further goal of the study is to show that the reliability of inheritance inference depends crucially on which sorts of base classes are used in making inferences. One approach to inheritance inference treats the extension of any atomic predicate as a suitable base class. A second approach identifies suitable base classes with the cells of a partition (of a preselected size k) of the domain of objects that satisfies the condition of maximizing the similarity of objects that are assigned to the same class. In addition to permitting more inferences, our study shows that the second approach results in inheritance inferences that are far more reliable, particularly in the case of exceptional subclasses.

This article defines a family of inference relations which aim at reasoning with inconsistent knowledge bases. These inference relations are defined out of inconsistency measures. We check under which conditions the new inference relations satisfy a series of properties for nonmonotonic reasoning. We also show that they are paraconsistent when the corresponding inconsistency measures satisfy some rationality postulates. Besides, we show some dependencies and incompatibilities among some rationality postulates.

We propose a novel formal framework (called 3D-nCDC-ASP) to represent and reason about cardinal directions between extended objects in 3-dimensional (3D) space, using Answer Set Programming (ASP). 3D-nCDC-ASP extends Cardinal Directional Calculus (CDC) with a new type of default constraints, and nCDC-ASP to 3D. 3D-nCDC-ASP provides a flexible platform offering different types of reasoning: Nonmonotonic reasoning with defaults, checking consistency of a set of constraints on 3D cardinal directions between objects, explaining inconsistencies, and inferring missing CDC relations. We prove the soundness of 3D-nCDC-ASP, and illustrate its usefulness with applications. This paper is under consideration for acceptance in TPLP., Paper presented at the 36th International Conference on Logic Programming (ICLP 2020), University Of Calabria, Rende (CS), Italy, September 2020, 29 pages, 6 figures

Default logic is one of the basic formalisms for nonmonotonic reasoning, a well-established area from logic-based artificial intelligence dealing with the representation of rational conclusions, which are characterised by the feature that the inference process may require to retract prior conclusions given additional premisses. This nonmonotonic aspect is in contrast to valid inference relations, which are monotonic. Although nonmonotonic reasoning has been extensively studied in the literature, only few works exist dealing with a proper proof theory for specific logics. In this paper, we introduce sequent-type calculi for two variants of default logic, viz., on the one hand, for three-valued default logic due to Radzikowska, and on the other hand, for disjunctive default logic, due to Gelfond, Lifschitz, Przymusinska, and Truszczyński. The first variant of default logic employs ukasiewicz’s three-valued logic as the underlying base logic and the second variant generalises defaults by allowing a selection of consequents in defaults. Both versions have been introduced to address certain representational shortcomings of standard default logic. The calculi we introduce axiomatise brave reasoning for these versions of default logic, which is the task of determining whether a given formula is contained in some extension of a given default theory. Our approach follows the sequent method first introduced in the context of nonmonotonic reasoning by Bonatti, which employs a rejection calculus for axiomatising invalid formulas, taking care of expressing the consistency condition of defaults.

We study the complexity of the inference problem for propositional circumscription (the minimal inference problem) over arbitrary finite domains. The problem is of fundamental importance in nonmonotonic logics and commonsense reasoning. The complexity of the problem for the two-element domain has been completely classified. In this article, we classify the complexity of the problem over all conservative languages. We consider a version of the problem parameterized by a set of relations (a constraint language), from which we are allowed to build a knowledge base, and where a linear order used to compare models is a part of an input. We show that in this setting the problem is either Π P 2 -complete, coNP-complete, or in P. The classification is based on a coNP-hardness proof for a new class of languages, an analysis of languages that do not express any member of the class, and a new general polynomial-time algorithm solving the minimal inference problem for a large class of languages.

Answer Set Programming (ASP) is a well-known declarative problem solving approach based on nonmonotonic logic programs, which has been successfully applied to a wide range of applications in artificial intelligence and beyond. To address the needs of modern applications, HEX-programs were introduced as an extension of ASP with external atoms for accessing information outside programs via an API style bi-directional interface mechanism. To evaluate such programs, conflict-driving learning algorithms for SAT and ASP solving have been extended in order to capture the semantics of external atoms. However, a drawback of the state-of-the-art approach is that external atoms are only evaluated under complete assignments (i.e., input to the external source) while in practice, their values often can be determined already based on partial assignments alone (i.e., from incomplete input to the external source). This prevents early backtracking in case of conflicts, and hinders more efficient evaluation of HEX-programs. We thus extend the notion of external atoms to allow for three-valued evaluation under partial assignments, while the two-valued semantics of the overall HEX-formalism remains unchanged. This paves the way for three enhancements: first, to evaluate external sources at any point during model search, which can trigger learning knowledge about the source behavior and/or early backtracking in the spirit of theory propagation in SAT modulo theories (SMT). Second, to optimize the knowledge learned in terms of so-called nogoods, which roughly speaking are impossible input-output configurations. Shrinking nogoods to their relevant input part leads to more effective search space pruning. And third, to make a necessary minimality check of candidate answer sets more efficient by exploiting early external evaluation calls. As this check usually accounts for a large share of the total runtime, optimization is here particularly important. We further present an experimental evaluation of an implementation of a novel HEX-algorithm that incorporates these enhancements using a benchmark suite. Our results demonstrate a clear efficiency gain over the state-of-the-art HEX-solver for the benchmarks, and provide insights regarding the most effective combinations of solver configurations.

Issue title: Special Issue on the 30th Italian Conference on Computational Logic: CILC 2015Guest editors: Marco Maratea, Viviana Mascardi, Davide Ancona and Alberto Pettorossi; International audience; We explore the extension of the notion of rational closure to logics lacking the finite model property, considering the logic SHIQ. We provide a semantic characterization of rational closure in SHIQ in terms of a preferential semantics, based on a finite rank characterization of minimal models. We show that the rational closure of a KB can be computed in EXPTIME based on a polynomial encoding of the rational extension of SHIQ into entailment in SHIQ. We discuss the extension of rational closure to more expressive description logics.

Answer Set Programming (ASP) is a well-established paradigm for declarative programming and nonmonotonic reasoning. ASP allows for flexible modeling using rules. ASP rules induce a set of intended models called answer sets. Incoherence, the non-existence of answer sets, is therefore a feature of ASP, indicating that the rules admit no intended models. However, this feature can also be problematic in certain circumstances: errors that cause incoherence are notoriously difficult to debug, and query answering will not provide any meaningful answers for incoherent programs. Paracoherent semantics have been suggested as a remedy. They extend the classical notion of answer sets to draw meaningful conclusions also from incoherent programs. However, paracoherent semantics have essentially been inapplicable in practice, due to the lack of efficient algorithms and implementations. In this paper, this lack is addressed, and several different algorithms to compute semi-stable and semi-equilibrium models are proposed and implemented within an answer set solving framework. A key role in the framework is played by syntactic program transformations that allow for characterizing paracoherent semantics in terms of the answer sets of transformed programs. Apart from existing transformations from the literature, a novel transformation is also proposed, which provides an alternative characterization of paracoherent semantics in terms of (extended) externally supported models. Notably, the new transformation is more compact than the existing ones, and brings performance benefits. An extensive empirical performance comparison among the algorithms on benchmarks from ASP competitions and a real-world use case is given as well. It shows not only that the methods developed in this paper lead to practically effective systems, but also show a clear advantage of the methods that rely on (extended) externally supported models.

The paper proposes a model for the information retrieval system (E-library) for the learner, based on his current requirements and scenario. It follows a brokerage model using non monotonic logic utilizing semantics and ontology for object description. Ontology captures the learning object properties which can help in eliminating and evaluating the usefulness of the object for a given learner. Non monotonic logic helps in inferring the current usefulness of the learning object with current requirement and rules. It will vary the results with time and person. Therefore, it can provide better user oriented search.

The negative zombie argument states that p&~q is ideally negatively conceivable and, therefore, possible, what would entail that physicalism is false (Chalmers, 2002, 2010}. In the argument, p is the conjunction of the fundamental physical truths and laws and $q$ is a phenomenal truth. A sentence phi is ideally negatively conceivable iff phi cannot be ruled out a priori on ideal rational reflection. In this paper, I argue that if its premises are true, the negative zombie argument is neither conclusive (valid) nor a priori. First, I argue that the argument is sound iff there exists a finite ideal reasoner R for a logic x with the relevant properties which believes <>(p&~q) on the basis of not believing p->q on a priori basis. A finite reasoner is a reasoner with finite memory and finite computational power. I argue that if x has the relevant properties and R is finite, then x must be nonmonotonic and R may only approach ideallity at the limit of a reasoning sequence. This would render the argument nonconclusive. Finally, I argue that, for some q, R does not believe <>(p&~q) on the basis of not believing p->q on a priori basis. For example, for q=`someone is conscious'. I conclude that the negative zombie argument (and, maybe, all zombie arguments) is neither conclusive nor a priori (the choice of q relies on empirical information). The negative zombie argument states that p&~q is ideally negatively conceivable and, therefore, possible, what would entail that physicalism is false (Chalmers, 2002, 2010}. In the argument, p is the conjunction of the fundamental physical truths and laws and $q$ is a phenomenal truth. A sentence phi is ideally negatively conceivable iff phi cannot be ruled out a priori on ideal rational reflection. In this paper, I argue that if its premises are true, the negative zombie argument is neither conclusive (valid) nor a priori. First, I argue that the argument is sound iff there exists a finite ideal reasoner R for a logic x with the relevant properties which believes <>(p&~q) on the basis of not believing p->q on a priori basis. A finite reasoner is a reasoner with finite memory and finite computational power. I argue that if x has the relevant properties and R is finite, then x must be nonmonotonic and R may only approach ideallity at the limit of a reasoning sequence. This would render the argument nonconclusive. Finally, I argue that, for some q, R does not believe <>(p&~q) on the basis of not believing p->q on a priori basis. For example, for q=`someone is conscious'. I conclude that the negative zombie argument (and, maybe, all zombie arguments) is neither conclusive nor a priori (the choice of q relies on empirical information).

A propositional conditional of the form ( B | A ) , representing the default rule “If A , then usually B ”, goes beyond the limits of classical logic, and the semantics of a knowledge base consisting of such conditionals must take into account the three-valued nature of conditionals. Ordinal conditional functions (OCF), also called ranking functions, assign a degree of implausibility to possible worlds and provide a convenient semantic framework for conditionals. To each consistent knowledge base R , system Z associates a unique minimal OCF accepting R , enabling inductive reasoning from this model. In this article, we present an approach of transforming the ideas of the popular system Z to the first-order case. We develop system Z FO that considers first-order conditionals of the form ( B ( x ) | A ( x ) ) . The notion of tolerance used in system Z is extended to the notion of tolerance pairs, taking also a partition of the domain elements into account. We show that each tolerance pair induces a system Z-like ranking function, and we provide an algorithm systematically generating all tolerance pairs. We introduce the notion of minimal tolerance pairs and a corresponding refinement of the algorithm computing all minimal tolerance pairs. An inference relation based on minimal tolerance pairs is presented, and it is shown that system Z FO properly generalizes the basic ideas underlying system Z.

The purpose based access control model has been proposed recently to restrict the access to the sensitive data which are out of control of their owner. This model can be enforced by ensuring that the user who wants to access the private data will respect the specific plan of tasks/actions that leads to achieving the intended objective to use these data. The Organization Based Access Control (OrBAC) model is suitable to integrate this principle, but in a dynamic environment such as the cloud computing, the authorization rules should be expressed in flexible way, and they may include optional tasks which can be skipped in some cases in order to adapt temporarily to the changes in the context. To meet these requirements, we propose in this paper a new extension of the OrBAC model using the temporal nonmonotonic description logic ( $\textit {TL-JClassic}^{+}_{\delta \epsilon }$ ) that allows to represent formally the policy rules as hierarchical planning that includes a set of ordered tasks that may admit exceptions in special cases and when the access request is made, the access control system depending on the current context will infer dynamically the appropriate sequence of actions that can be performed by subject who demands access to private data that may be outsourced into the cloud.

Most of reasoning for decision making in daily life is based on preferences. As other kinds of reasoning processes, there are many formalisms trying to capture preferences, however none of them is able to capture all the subtleties of the human reasoning. In this paper we analyze how to formalize the preferences expressed by humans and how to reason with them to produce rankings. Particularly, we show that qualitative preferences are best represented with a combination of reward logics and conditional logics. We propose a new algorithm based on ideas of similarity between objects commonly used in case-based reasoning. We see that the new approach produces rankings close to the ones expressed by users. © 2016 Elsevier B.V., This research is partially funded by the CSIC Intramural projects RPREF (201650E044) and AMIDA (201450E009), the Spanish MICINN projects EdeTRI (TIN2012-39348-C02-01) and MILESS (TIN2013-45039-P), and the grant 2014-SGR-118 from the Generalitat de Catalunya

Formalising deontic concepts, such as obligation, prohibition and permission, is normally carried out in a modal logic with a possible world semantics, in which some worlds are better than others. The main focus in these logics is on inferring logical consequences, for example inferring that the obligation O q is a logical consequence of the obligations O p and O (p → q). In this paper we propose a non-modal approach in which obligations are preferred ways of satisfying goals expressed in first-order logic. To say that p is obligatory, but may be violated, resulting in a less than ideal situation s, means that the task is to satisfy the goal p ∨ s, and that models in which p is true are preferred to models in which s is true. Whereas, in modal logic, the preference relation between possible worlds is part of the semantics of the logic, in this non-modal approach, the preference relation between first-order models is external to the logic. Although our main focus is on satisfying goals, we also formulate a notion of logical consequence, which is comparable to the notion of logical consequence in modal deontic logic. In this formalisation, an obligation O p is a logical consequence of goals G, when p is true in all best models of G. We show how this non-modal approach to the treatment of deontic concepts deals with problems of contrary-to-duty obligations and normative conflicts, and argue that the approach is useful for many other applications, including abductive explanations, defeasible reasoning, combinatorial optimisation, and reactive systems of the production system variety.