The introduction of explicit notions of rejection, or disbelief, into logics for knowledge representation can be justiﬁed in a number of ways. Motivations range from the need for versions of negation weaker than classical negation, to the explicit recording of classic belief contraction operations in the area of belief change, and the additional levels of expressivity obtained from an extended version of belief change which includes disbelief contraction. In this paper we present four logics of disbelief which (...) address some or all of these intuitions. Soundness and completeness results are supplied and the logics are compared with respect to applicability and utility. (shrink)
We present a model for ﬁrst-order belief revision that is characterized by an underlying relevance-like relation and a background proof system. The model is extremely general in order to allow for a wide variety in these characterizing parameters. It allows some weakenings of beliefs which were initially implicit to become explicit and survive the revision process. The effects of revision are localized to the part of the theory that is inﬂuenced by the the new information. Iterated revision in this model (...) is handled trivially since the revision operator is constructive by deﬁnition. The usage of deductively limited proof systems permits an inconsistency tolerant model. The notion of a part of a theory capable of being inﬂuenced by new information (designed to accomodate the speciﬁc character of ﬁrst-order languages) is shown to satisfy some intuitive and desirable properties. We show that for particular parametrizations, standard revision schemes can be embedded into our paradigm. (shrink)
We propose a new relevance sensitive model for representing and revising belief structures, which relies on a notion of partial language splitting and tolerates some amount of inconsistency while retaining classical logic. The model preserves an agent's ability to answer queries in a coherent way using Belnap's four-valued logic. Axioms analogous to the AGM axioms hold for this new model. The distinction between implicit and explicit beliefs is represented and psychologically plausible, computationally tractable procedures for query answering and belief..
Possible-world semantics are provided for Parikh’s relevance-sensitive model for belief revision. Having Grove’s system-of-spheres construction as a base, we consider additional constraints on measuring distance between possible worlds, and we prove that, in the presence of the AGM postulates, these constraints characterize precisely Parikh’s axiom (P). These additional constraints essentially generalize a criterion of similarity that predates axiom (P) and was originally introduced in the context of Reasoning about Action. A by-product of our study is the identiﬁcation of two possible (...) readings of Parikh’s axiom (P), which we call the strong and the weak versions of the axiom. An interesting feature of the strong version is that, unlike classical AGM belief revision, it makes associations between the revision policies of different theories. (shrink)
validity of attributes that have been suggested as pointers of personand obligations on behalf of his household; his wife and children hood, and conclude that they will take their place within a broader were only indirectly the subject of legal rights and his slaves were matrix of pragmatic, philosophical and extra-legal concepts.
Software is much more than sequences of instructions for a computing machine: it can be an enabler (or disabler) of political imperatives and policies. Hence, it is subject to the same assessment in a normative dimension as other political and social phenomena. The core distinction between free software and its proprietary counterpart is that free software makes available to its user the knowledge and innovation contributed by the creator(s) of the software, in the form of the created source code. From (...) an ethical perspective, one of the most pressing questions raised by this form of collaboration is the question of the rights, and the restrictions on them, that are passed on to users and collaborators by the creators of programs. That is, what freedoms do software users deserve, and how can they best be protected? In this study we analyze free software licensing schemes in order to determine which most effectively protects such freedoms. We conclude that so-called copyleft licensing schemes are the morally superior alternative. (shrink)
Dept of Business Administration Dept of Computer and Knowledge Systems Group University of Patras Information Science School of Computer Science 265 00 Patras, Greece Brooklyn College of the and Engineering firstname.lastname@example.org City University of New York University of New South Wales Brooklyn, NY 11210, USA Sydney, NSW 2052, Australia email@example.com firstname.lastname@example.org..
The “free” in “free software” refers to a cluster of four specific freedoms identified by the Free Software Definition. The first freedom, termed “Freedom Zero,” intends to protect the right of the user to deploy software in whatever fashion, towards whatever end, he or she sees fit. But software may be used to achieve ethically questionable ends. This highlights a tension in the provision of software freedoms: while the definition explicitly forbids direct restrictions on users’ freedoms, it does not address (...) other means by which software may indirectly restrict freedoms. In particular, ethically-inflected debate has featured prominently in the discussion of restrictions on digital rights management and privacy-violating code in version 3 of the GPL (GPLv3). The discussion of this proposed language revealed the spectrum of ethical positions and valuations held by members of the free software community. In our analysis, we will provide arguments for upholding Freedom Zero; we embed the problem of possible uses of software in the broader context of the uses of scientific knowledge, and go on to argue that the provision of Freedom Zero mitigates against too great a moral burden—of anticipating possible uses of software—being placed on the programmer and that, most importantly, it facilitates deliberative discourse in the free software community. (shrink)
The axiom of recovery, while capturing a central intuition regarding belief change, has been the source of much controversy. We argue briefly against putative counterexamples to the axiom—while agreeing that some of their insight deserves to be preserved—and present additional recovery-like axioms in a framework that uses epistemic states, which encode preferences, as the object of revisions. This makes iterated revision possible and renders explicit the connection between iterated belief change and the axiom of recovery. We provide a representation theorem (...) that connects the semantic conditions we impose on iterated revision and our additional syntactical properties. We show interesting similarities between our framework and that of Darwiche–Pearl (Artificial Intelligence 89:1–29 1997). In particular, we show that intuitions underlying the controversial (C2) postulate are captured by the recovery axiom and our recovery-like postulates (the latter can be seen as weakenings of (C2)). We present postulates for contraction, in the same spirit as the Darwiche–Pearl postulates for revision, and provide a theorem that connects our syntactic postulates with a set of semantic conditions. Lastly, we show a connection between the contraction postulates and a generalisation of the recovery axiom. (shrink)
We provide a formal study of belief retraction operators that do not necessarily satisfy the (Inclusion) postulate. Our intuition is that a rational description of belief change must do justice to cases in which dropping a belief can lead to the inclusion, or ‘liberation’, of others in an agent's corpus. We provide two models of liberation via retraction operators: ρ-liberation and linear liberation. We show that the class of ρ-liberation operators is included in the class of linear ones and provide (...) axiomatic characterisations for each class. We show how any retraction operator (including the liberation operators) can be ‘converted’ into either a withdrawal operator (i.e., satisfying (Inclusion)) or a revision operator via (a slight variant of) the Harper Identity and the Levi Identity respectively. (shrink)
Traditional accounts of belief change have been criticized for placing undue emphasis on the new belief provided as input. A recent proposal to address such issues is a framework for non-prioritized belief change based on default theories (Ghose and Goebel, 1998). A novel feature of this approach is the introduction of disbeliefs alongside beliefs which allows for a view of belief contraction as independently useful, instead of just being seen as an intermediate step in the process of belief revision. This (...) approach is, however, restrictive in assuming a linear ordering of reliability on the received inputs. In this paper, we replace the linear ordering with a preference ranking on inputs from which a total preorder on inputs can be induced. This extension brings along with it the problem of dealing with inputs of equal rank. We provide a semantic solution to this problem which contains, as a special case, AGM belief change on closed theories. (shrink)
We present a framework that provides a logic for science by generalizing the notion of logical (Tarskian) consequence. This framework will introduce hierarchies of logical consequences, the first level of each of which is identified with deduction. We argue for identification of the second level of the hierarchies with inductive inference. The notion of induction presented here has some resonance with Popper's notion of scientific discovery by refutation. Our framework rests on the assumption of a restricted class of structures in (...) contrast to the permissibility of classical first-order logic. We make a distinction between deductive and inductive inference via the notions of compactness and weak compactness. Connections with the arithmetical hierarchy and formal learning theory are explored. For the latter, we argue against the identification of inductive inference with the notion of learnable in the limit. Several results highlighting desirable properties of these hierarchies of generalized logical consequence are also presented. (shrink)