The new field of judgment aggregation aims to merge many individual sets of judgments on logically interconnected propositions into a single collective set of judgments on these propositions. Judgment aggregation has commonly been studied using classical propositional logic, with a limited expressive power and a problematic representation of conditional statements ("if P then Q") as material conditionals. In this methodological paper, I present a simple unified model of judgment aggregation in general logics. I show (...) how many realistic decision problems can be represented in it. This includes decision problems expressed in languages of classical propositional logic, predicate logic (e.g. preference aggregation problems), modal or conditional logics, and some multi-valued or fuzzy logics. I provide a list of simple tools for working with general logics, and I prove impossibility results that generalise earlier theorems. (shrink)

In the framework of judgment aggregation, we assume that some formulas of the agenda are singled out as premisses, and that both Independence (formula-wise aggregation) and Unanimity Preservation hold for them. Whether premiss-based aggregation thus defined is compatible with conclusion-based aggregation, as defined by Unanimity Preservation on the non-premisses, depends on how the premisses are logically connected, both among themselves and with other formulas. We state necessary and sufficient conditions under which the combination of both (...) approaches leads to dictatorship (resp. oligarchy), either just on the premisses or on the whole agenda. This framework is inspired by the doctrinal paradox of legal theory and arguably relevant to this field as well as political science and political economy. When the set of premisses coincides with the whole agenda, a limiting case of our assumptions, we obtain several existing results in judgment aggregation theory. (shrink)

Cognitivists and non-cognitivists in contemporary meta-ethics tend to assume that moral judgments are semantically uniform. That is, they share the assumption that either all moral judgments express beliefs, or they all express non-beliefs. But what if some moral judgments express beliefs and others do not? Then moral judgments are not semantically uniform and the question “Cognitivist or non-cognitivist?” poses a false dilemma. I will question the assumption that moral judgments are semantically uniform. First, I will explain what I mean by (...) the assumption (section 2). I will call this assumption SUM, the semantic uniformity of moral judgments. Second, I will provide some examples in order to illustrate that SUM cannot be taken for granted (section 3). Third, I will try to understand, using ideas from Wittgenstein, why SUM has nevertheless so often been taken for granted (section 4). Fourth, I will discuss some authors in contemporary meta-ethics who have noted the false dilemma between cognitivism and non-cognitivism and evaluate the solutions they propose for overcoming it (section 5). Fifth, I will indicate, again with some help from Wittgenstein, how meta-ethical research about moral judgments is possible without the assumption that morality is semantically uniform (section 6). (shrink)

Group decisions must often obey exogenous constraints. While in a preference aggregation problem constraints are modelled by restricting the set of feasible alternatives, this paper discusses the modelling of constraints when aggregating individual yes/no judgments on interconnected propositions. For example, court judgments in breach-of-contract cases should respect the constraint that action and obligation are necessary and sufficient for liability, and judgments on budget items should respect budgetary constraints. In this paper, we make constraints in judgment aggregation explicit (...) by relativizing the rationality conditions of consistency and deductive closure to a constraint set, whose variation yields more or less strong notions of rationality. This approach of modelling constraints explicitly contrasts with that of building constraints as axioms into the logic, which turns compliance with constraints into a matter of logical consistency and thereby conflates requirements of ordinary logical consistency and requirements dictated by the environment . We present some general impossibility results on constrained judgment aggregation; they are immediate corollaries of known results on judgment aggregation. (shrink)

Health Level 7 (HL7) is an international standards development organisation in the domain of healthcare information technology. Initially the mission of HL7 was to enable data exchange via the creation of syntactic standards which supported point-to-point messaging. Currently HL7 sees its mission as one of creating standards for semantic interoperability in healthcare IT on the basis of its flagship “version 3” (v3). Unfortunately, v3 has been plagued by quality and consistency issues, and it has not been able to (...) keep pace with recent developments either in semantics and ontology or in computer science and engineering. HL7’s response has been to develop its “Services-Aware Interoperability Framework” (SAIF), which is intended to provide a foundation for work on all aspects of standardization in HL7 henceforth. We here summarise the major design principles that must be satisfied by a semantic interoperability framework – principles relating both to static semantics and to computational behaviour. We then assess the SAIF in light of these principles. We conclude that the SAIF is not in a position to support the needed reform of the HL7 v3 family of standards. (shrink)

This chapter briefly reviews the present state of judgment aggregation theory and tentatively suggests a future direction for that theory. In the review, we start by emphasizing the difference between the doctrinal paradox and the discursive dilemma, two idealized examples which classically serve to motivate the theory, and then proceed to reconstruct it as a brand of logical theory, unlike in some other interpretations, using a single impossibility theorem as a key to its technical development. In the prospective (...) part, having mentioned existing applications to social choice theory and computer science, which we do not discuss here, we consider a potential application to law and economics. This would be based on a deeper exploration of the doctrinal paradox and its relevance to the functioning of collegiate courts. On this topic, legal theorists have provided empirical observations and theoretical hints that judgment aggregation theorists would be in a position to clarify and further elaborate. As a general message, the chapter means to suggest that the future of judgment aggregation theory lies with its applications rather than its internal theoretical development. (shrink)

In this article I give an overview of some recent work in philosophy of science dedicated to analysing the scientific process in terms of (conceptual) mathematical models of theories and the various semantic relations between such models, scientific theories, and aspects of reality. In current philosophy of science, the most interesting questions centre around the ways in which writers distinguish between theories and the mathematical structures that interpret them and in which they are true, i.e. between scientific theories as (...) linguistic systems and their non-linguistic models. In philosophy of science literature there are two main approaches to the structure of scientific theories, the statement or syntactic approach -- advocated by Carnap, Hempel and Nagel -- and the non- statement or semantic approach --advocated, among others, by Suppes, the structuralists, Beth, Van Fraassen, Giere, Wojcicki. In conclusion, I briefly review some of the usual realist inspired questions about the possibility and character of relations between scientific theories and reality as implied by the various approaches I discuss in the course of the article. The models of a scientific theory should indeed be adequate to the phenomena, but if the theory is 'adequate' to (true in) its conceptual (mathematical) models as well, we have a model-theoretic realism that addresses the possible meaning and reference of 'theoretical entities' without relapsing into the metaphysics typical of the usual scientific realist approaches. (shrink)

The logicality of language is the hypothesis that the language system has access to a ‘natural’ logic that can identify and filter out as unacceptable expressions that have trivial meanings—that is, that are true/false in all possible worlds or situations in which they are defined. This hypothesis helps explain otherwise puzzling patterns concerning the distribution of various functional terms and phrases. Despite its promise, logicality vastly over-generates unacceptability assignments. Most solutions to this problem rest on specific stipulations about the properties (...) of logical form—roughly, the level of linguistic representation which feeds into the interpretation procedures—and have substantial implications for traditional philosophical disputes about the nature of language. Specifically, contextualism and semantic minimalism, construed as competing hypotheses about the nature and degree of context-sensitivity at the level of logical form, suggest different approaches to the over-generation problem. In this paper, I explore the implications of pairing logicality with various forms of contextualism and semantic minimalism. I argue that to adequately solve the over-generation problem, logicality should be implemented in a constrained contextualist framework. (shrink)

The aim of the paper is to develop general criteria of argumentative validity and adequacy for probabilistic arguments on the basis of the epistemological approach to argumentation. In this approach, as in most other approaches to argumentation, proabilistic arguments have been neglected somewhat. Nonetheless, criteria for several special types of probabilistic arguments have been developed, in particular by Richard Feldman and Christoph Lumer. In the first part (sects. 2-5) the epistemological basis of probabilistic arguments is discussed. With regard (...) to the philosophical interpretation of probabilities a new subjectivist, epistemic interpretation is proposed, which identifies probabilities with tendencies of evidence (sect. 2). After drawing the conclusions of this interpretation with respect to the syntactic features of the probability concept, e.g. one variable referring to the data base (sect. 3), the justification of basic probabilities (priors) by judgements of relative frequency (sect. 4) and the justification of derivative probabilities by means of the probability calculus are explained (sect. 5). The core of the paper is the definition of '(argumentatively) valid derivative probabilistic arguments', which provides exact conditions for epistemically good probabilistic arguments, together with conditions for the adequate use of such arguments for the aim of rationally convincing an addressee (sect. 6). Finally, some measures for improving the applicability of probabilistic reasoning are proposed (sect. 7). (shrink)

A precise formulation of the structure of modern evolutionary theory has proved elusive. In this paper, I introduce and develop a formal approach to the structure of population genetics, evolutionary theory's most developed sub-theory. Under the semantic approach, used as a framework in this paper, presenting a theory consists in presenting a related family of models. I offer general guidelines and examples for the classification of population genetics models; the defining features of the models are taken to (...) be their state spaces, parameters, and laws. The suggestions regarding the various aspects of the characterization of population genetics models provide an outline for further detailed research. (shrink)

This article concentrates on a couple of semiotic approaches working out, on the one hand, the mediated character of reducing interpretative trajectories to the actual translation into the language of narratives (A. J. Greimas) or the language of textuality (F. Rastier), and, on the other, the direct, apparently unmediated passage to the visceral physicality of the verbal signifying system, which make semantic and syntactic components perfunctory to interpretation in a way (J. Kristeva). Greimassian universal narrative grammar dismantles signifying (...) units, navigating in the network of narrative utterances. Rastier's approach structures textual artifacts by unearthing semantic constituents crucial for semiotic analysis. Kristeva examines what is behind the curtain instead of sorting out the significance of the text's content as a special category and the possibility of procedure allowing its interpretation. These three authors are compared in the context of two approaches that come to grips with the author/reader pair. (shrink)

Political theorists have offered many accounts of collective decision-making under pluralism. I discuss a key dimension on which such accounts differ: the importance assigned not only to the choices made but also to the reasons underlying those choices. On that dimension, different accounts lie in between two extremes. The ‘minimal liberal account’ holds that collective decisions should be made only on practical actions or policies and that underlying reasons should be kept private. The ‘comprehensive deliberative account’ stresses the importance of (...) giving reasons for collective decisions, where such reasons should also be collectively decided. I compare these two accounts on the basis of a formal model developed in the growing literature on the ‘discursive dilemma’ and ‘judgment aggregation’ and address several questions: What is the trade-off between the (minimal liberal) demand for reaching agreement on outcomes and the (comprehensive deliberative) demand for reason-giving? How large should the ‘sphere of public reason’ be? When do the decision procedures suggested by the two accounts agree and when not? How good are these procedures at truthtracking on factual matters? What strategic incentives do they generate for decision-makers? My discussion identifies what is at stake in the choice between minimal liberal and comprehensive deliberative accounts of collective decisionmaking, and sheds light not only on these two ideal-typical accounts themselves, but also on many characteristics that intermediate accounts share with them. (shrink)

Axiom weakening is a novel technique that allows for fine-grained repair of inconsistent ontologies. In a multi-agent setting, integrating ontologies corresponding to multiple agents may lead to inconsistencies. Such inconsistencies can be resolved after the integrated ontology has been built, or their generation can be prevented during ontology generation. We implement and compare these two approaches. First, we study how to repair an inconsistent ontology resulting from a voting-based aggregation of views of heterogeneous agents. Second, we prevent the generation (...) of inconsistencies by letting the agents engage in a turn-based rational protocol about the axioms to be added to the integrated ontology. We instantiate the two approaches using real-world ontologies and compare them by measuring the levels of satisfaction of the agents w.r.t. the ontology obtained by the two procedures. (shrink)

This paper presents a uniform semantic treatment of nonmonotonic inference operations that allow for inferences from infinite sets of premises. The semantics is formulated in terms of selection functions and is a generalization of the preferential semantics of Shoham (1987), (1988), Kraus, Lehman, and Magidor (1990) and Makinson (1989), (1993). A selection function picks out from a given set of possible states (worlds, situations, models) a subset consisting of those states that are, in some sense, the most preferred ones. (...) A proposition α is a nonmonotonic consequence of a set of propositions Γ iff α holds in all the most preferred Γ-states. In the literature on revealed preference theory, there are a number of well-known theorems concerning the representability of selection functions, satisfying certain properties, in terms of underlying preference relations. Such theorems are utilized here to give corresponding representation theorems for nonmonotonic inference operations. At the end of the paper, the connection between nonmonotonic inference and belief revision, in the sense of Alchourrón, Gärdenfors, and Makinson, is explored. In this connection, infinitary belief revision operations that allow for the revision of a theory with a possibly infinite set of propositions are introduced and characterized axiomatically. (shrink)

Judgment aggregation theory, or rather, as we conceive of it here, logical aggregation theory generalizes social choice theory by having the aggregation rule bear on judgments of all kinds instead of merely preference judgments. It derives from Kornhauser and Sager’s doctrinal paradox and List and Pettit’s discursive dilemma, two problems that we distinguish emphatically here. The current theory has developed from the discursive dilemma, rather than the doctrinal paradox, and the final objective of the paper is (...) to give the latter its own theoretical development along the line of recent work by Dietrich and Mongin. However, the paper also aims at reviewing logical aggregation theory as such, and it covers impossibility theorems by Dietrich, Dietrich and List, Dokow and Holzman, List and Pettit, Mongin, Nehring and Puppe, Pauly and van Hees, providing a uniform logical framework in which they can be compared with each other. The review goes through three historical stages: the initial paradox and dilemma, the scattered early results on the independence axiom, and the so-called canonical theorem, a collective achievement that provided the theory with its specific method of analysis. The paper goes some way towards philosophical logic, first by briefly connecting the aggregative framework of judgment with the modern philosophy of judgment, and second by thoroughly discussing and axiomatizing the ‘general logic’ built in this framework. (shrink)

How can the propositional attitudes of several individuals be aggregated into overall collective propositional attitudes? Although there are large bodies of work on the aggregation of various special kinds of propositional attitudes, such as preferences, judgments, probabilities and utilities, the aggregation of propositional attitudes is seldom studied in full generality. In this paper, we seek to contribute to filling this gap in the literature. We sketch the ingredients of a general theory of propositional attitude aggregation and prove (...) two new theorems. Our first theorem simultaneously characterizes some prominent aggregation rules in the cases of probability, judgment and preference aggregation, including linear opinion pooling and Arrovian dictatorships. Our second theorem abstracts even further from the specific kinds of attitudes in question and describes the properties of a large class of aggregation rules applicable to a variety of belief-like attitudes. Our approach integrates some previously disconnected areas of investigation. (shrink)

Decision-making typically requires judgments about causal relations: we need to know the causal effects of our actions and the causal relevance of various environmental factors. We investigate how several individuals' causal judgments can be aggregated into collective causal judgments. First, we consider the aggregation of causal judgments via the aggregation of probabilistic judgments, and identify the limitations of this approach. We then explore the possibility of aggregating causal judgments independently of probabilistic ones. Formally, we introduce the problem (...) of causal-network aggregation. Finally, we revisit the aggregation of probabilistic judgments when this is constrained by prior aggregation of qualitative causal judgments. (shrink)

The aggregation of individual judgments over interrelated propositions is a newly arising field of social choice theory. I introduce several independence conditions on judgment aggregation rules, each of which protects against a specific type of manipulation by agenda setters or voters. I derive impossibility theorems whereby these independence conditions are incompatible with certain minimal requirements. Unlike earlier impossibility results, the main result here holds for any (non-trivial) agenda. However, independence conditions arguably undermine the logical structure of (...) class='Hi'>judgment aggregation. I therefore suggest restricting independence to premises, which leads to a generalised premise-based procedure. This procedure is proven to be possible if the premises are logically independent. (shrink)

لقد بُذلت محاولات عديدة لتجاوز غموض قضايا العلوم الطبيعية والإنسانية من قبل المناطقة وفلاسفة اللغة، لا سيما خلال القرن العشرين، لكن تبرز منها محاولتان أكثر أهمية من غيرهما؛ تجلت الأولى في تطوير المنطق الرمزي الكلاسيكي ثنائي القيم إلى ما يُعرف بالمنطق متعدد القيم. ووفقًا لهذا الأخير لم يعد الحكم المنطقي – على أية قضية – مقصورًا على قيمتي الصدق التقليديتين: صادقة & كاذبة، كما يقضي بذلك قانون الثالث المرفوع، بل بات لدينا عدد لا متناه من القيم المتصلة التي تتوسط بين (...) الصدق التام والكذب التام. ورغم النجاح النسبي لهذه المحاولة – التي ما زالت تخضع للتطوير والتعديل – إلا أن المشكلة الأساسية ما زالت تطل برأسها في كل استخدام للكلمات وقضايا اللغة، فإذا كان المنطق متعدد القيم قد نجح في التعبير الواضح عن غموض المعرفة، إلا أنه لم يُبدد الغموض ذاته. أما المحاولة الثانية فقد تمثلت في نزعة التقييم الفائق، التي تفترض وجود عدد من التقييمات المقبولة لكل مصطلح غامض أو قضية غامضة. وليست هذه التقييمات في الحقيقة مجرد كيانات خالصة لا علاقة لها بالواقع، بل إن كل تقييم منها – كما تفترض النزعة – هو بمثابة تحديد لكيان واقعي نشير إليه بالاسم أو المصطلح محل الدراسة، ومن ثم فهو يعكس موجودًا فعليًا له حدوده الدقيقة المميزة له عن غيره. ويلزم عن ذلك أننا إذا كنا نقبل العديد من التقييمات المختلفة والمتنوعة لمصطلح واحد، فعلينا أن نقبل أيضًا وجود العديد من الكيانات الواقعية التي يشير إليها ذلك المصطلح الواحد. هذا ما نسعى إلى معالجته في هذا البحث، انطلاقًا من فرضٍ رئيس مؤداه أن ما واجه المنطق الكلاسيكي من مشكلات أدت إلى تطويره، لاسيما مشكلة الغموض، قد واجه بالمثل المنطق متعدد القيم، ولابد وأن يواجه أيضًا أية مقاربة مهما اختلفت أدواتها؛ فالغموض فيما نزعم ظاهرة إبستمولوجية في المحل الأول، مردودها إلى الذات العارفة وقصور إمكاناتها الإدراكية والقياسية، لا إلى الوجود ذاته. وبعبارة أخرى، نزعم من خلال هذه الورقة أن أية مقاربة لمشكلة الغموض ما هي إلا حلقة من حلقات العلاقة الجدلية اللامنتهية بين الإنسان والطبيعة، أو فلنقل بين ما هو مدرك وما هو موجود بالفعل. وقد ركزنا على قضايا وتصورات الجغرافيا كنموذج للتطبيق باعتبارها أحد أقرب العلوم الإنسانية إلى العلوم الطبيعية، وإن كنا نرى أن عمومية مشكلة الغموض – بأبعادها المختلفة – تُحيل أي علم إلى علم إنساني. (shrink)

Several recent results on the aggregation of judgments over logically connected propositions show that, under certain conditions, dictatorships are the only propositionwise aggregation functions generating fully rational (i.e., complete and consistent) collective judgments. A frequently mentioned route to avoid dictatorships is to allow incomplete collective judgments. We show that this route does not lead very far: we obtain oligarchies rather than dictatorships if instead of full rationality we merely require that collective judgments be deductively closed, arguably a minimal (...) condition of rationality, compatible even with empty judgment sets. We derive several characterizations of oligarchies and provide illustrative applications to Arrowian preference aggregation and Kasher and Rubinsteinís group identification problem. (shrink)

In solving judgment aggregation problems, groups often face constraints. Many decision problems can be modelled in terms the acceptance or rejection of certain propositions in a language, and constraints as propositions that the decisions should be consistent with. For example, court judgments in breach-of-contract cases should be consistent with the constraint that action and obligation are necessary and sufficient for liability; judgments on how to rank several options in an order of preference with the constraint of transitivity; and (...) judgments on budget items with budgetary constraints. Often more or less demanding constraints on decisions are imaginable. For instance, in preference ranking problems, the transitivity constraint is often contrasted with the weaker acyclicity constraint. In this paper, we make constraints explicit in judgment aggregation by relativizing the rationality conditions of consistency and deductive closure to a constraint set, whose variation yields more or less strong notions of rationality. We review several general results on judgment aggregation in light of such constraints. (shrink)

In the theory of judgment aggregation, it is known for which agendas of propositions it is possible to aggregate individual judgments into collective ones in accordance with the Arrow-inspired requirements of universal domain, collective rationality, unanimity preservation, non-dictatorship and propositionwise independence. But it is only partially known (e.g., only in the monotonic case) for which agendas it is possible to respect additional requirements, notably non-oligarchy, anonymity, no individual veto power, or implication preservation. We fully characterize the agendas for (...) which there are such possibilities, thereby answering the most salient open questions about propositionwise judgment aggregation. Our results build on earlier results by Nehring and Puppe (2002), Nehring (2006), Dietrich and List (2007a) and Dokow and Holzman (2010a). (shrink)

All existing impossibility theorems on judgment aggregation require individual and collective judgment sets to be consistent and complete, arguably a demanding rationality requirement. They do not carry over to aggregation functions mapping profiles of consistent individual judgment sets to consistent collective ones. We prove that, whenever the agenda of propositions under consideration exhibits mild interconnections, any such aggregation function that is "neutral" between the acceptance and rejection of each proposition is dictatorial. We relate this (...) theorem to the literature. (shrink)

This work contributes to the theory of judgement aggregation by discussing a number of significant non-classical logics. After adapting the standard framework of judgement aggregation to cope with non-classical logics, we discuss in particular results for the case of Intuitionistic Logic, the Lambek calculus, Linear Logic and Relevant Logics. The motivation for studying judgement aggregation in non-classical logics is that they offer a number of modelling choices to represent agents’ reasoning in aggregation problems. By studying judgement (...) aggregation in logics that are weaker than classical logic, we investigate whether some well-known impossibility results, that were tailored for classical logic, still apply to those weak systems. (shrink)

The widely discussed "discursive dilemma" shows that majority voting in a group of individuals on logically connected propositions may produce irrational collective judgments. We generalize majority voting by considering quota rules, which accept each proposition if and only if the number of individuals accepting it exceeds a given threshold, where different thresholds may be used for different propositions. After characterizing quota rules, we prove necessary and sufficient conditions on the required thresholds for various collective rationality requirements. We also consider sequential (...) quota rules, which ensure collective rationality by adjudicating propositions sequentially and letting earlier judgments constrain later ones. Sequential rules may be path-dependent and strategically manipulable. We characterize path-independence and prove its essential equivalence to strategy-proofness. Our results shed light on the rationality of simple-, super-, and sub-majoritarian decision-making. (shrink)

In response to recent work on the aggregation of individual judgments on logically connected propositions into collective judgments, it is often asked whether judgment aggregation is a special case of Arrowian preference aggregation. We argue for the converse claim. After proving two impossibility theorems on judgment aggregation (using "systematicity" and "independence" conditions, respectively), we construct an embedding of preference aggregation into judgment aggregation and prove Arrow’s theorem (stated for strict preferences) as (...) a corollary of our second result. Although we thereby provide a new proof of Arrow’s theorem, our main aim is to identify the analogue of Arrow’s theorem in judgment aggregation, to clarify the relation between judgment and preference aggregation, and to illustrate the generality of the judgment aggregation model. JEL Classi…cation: D70, D71.. (shrink)

The aim of this article is to introduce the theory of judgment aggregation, a growing interdisciplinary research area. The theory addresses the following question: How can a group of individuals make consistent collective judgments on a given set of propositions on the basis of the group members' individual judgments on them? I begin by explaining the observation that initially sparked the interest in judgment aggregation, the so-called "doctinal" and "discursive paradoxes". I then introduce the basic formal (...) model of judgment aggregation, which allows me to present some illustrative variants of a generic impossibility result. I subsequently turn to the question of how this impossibility result can be avoided, going through several possible escape routes. Finally, I relate the theory of judgment aggregation to other branches of aggregation theory. Rather than offering a comprehensive survey of the theory of judgment aggregation, I hope to introduce the theory in a succinct and pedagogical way, providing an illustrative rather than exhaustive coverage of some of its key ideas and results. (shrink)

We analyse the computational complexity of three problems in judgment aggregation: (1) computing a collective judgment from a profile of individual judgments (the winner determination problem); (2) deciding whether a given agent can influence the outcome of a judgment aggregation procedure in her favour by reporting insincere judgments (the strategic manipulation problem); and (3) deciding whether a given judgment aggregation scenario is guaranteed to result in a logically consistent outcome, independently from what the (...) judgments supplied by the individuals are (the problem of the safety of the agenda). We provide results both for specific aggregation procedures (the quota rules, the premisebased procedure, and a distance-based procedure) and for classes of aggregation procedures characterised in terms of fundamental axioms. (shrink)

The new …eld of judgment aggregation aims to …nd collective judgments on logically interconnected propositions. Recent impossibility results establish limitations on the possibility to vote independently on the propositions. I show that, fortunately, the impossibility results do not apply to a wide class of realistic agendas once propositions like “if a then b” are adequately modelled, namely as subjunctive implications rather than material implications. For these agendas, consistent and complete collective judgments can be reached through appropriate quota rules (...) (which decide propositions using acceptance thresholds). I characterise the class of these quota rules. I also prove an abstract result that characterises consistent aggregation for arbitrary agendas in a general logic. (shrink)

Standard impossibility theorems on judgment aggregation over logically connected propositions either use a controversial systematicity condition or apply only to agendas of propositions with rich logical connections. Are there any serious impossibilities without these restrictions? We prove an impossibility theorem without requiring systematicity that applies to most standard agendas: Every judgment aggregation function (with rational inputs and outputs) satisfying a condition called unbiasedness is dictatorial (or effectively dictatorial if we remove one of the agenda conditions). Our (...) agenda conditions are tight. When applied illustratively to (strict) preference aggregation represented in our model, the result implies that every unbiased social welfare function with universal domain is effectively dictatorial. (shrink)

This paper provides an introductory review of the theory of judgment aggregation. It introduces the paradoxes of majority voting that originally motivated the field, explains several key results on the impossibility of propositionwise judgment aggregation, presents a pedagogical proof of one of those results, discusses escape routes from the impossibility and relates judgment aggregation to some other salient aggregation problems, such as preference aggregation, abstract aggregation and probability aggregation. The present (...) illustrative rather than exhaustive review is intended to give readers new to the field of judgment aggregation a sense of this rapidly growing research area. (shrink)

The problem of merging several ontologies has important applications in the Semantic Web, medical ontology engineering and other domains where information from several distinct sources needs to be integrated in a coherent manner.We propose to view ontology merging as a problem of social choice, i.e. as a problem of aggregating the input of a set of individuals into an adequate collective decision. That is, we propose to view ontology merging as ontology aggregation. As a first step in this (...) direction, we formulate several desirable properties for ontology aggregators, we identify the incompatibility of some of these properties, and we define and analyse several simple aggregation procedures. Our approach is closely related to work in judgment aggregation, but with the crucial difference that we adopt an open world assumption, by distinguishing between facts not included in an agent’s ontology and facts explicitly negated in an agent’s ontology. (shrink)

Which rules for aggregating judgments on logically connected propositions are manipulable and which not? In this paper, we introduce a preference-free concept of non-manipulability and contrast it with a preference-theoretic concept of strategy-proofness. We characterize all non-manipulable and all strategy-proof judgment aggregation rules and prove an impossibility theorem similar to the Gibbard--Satterthwaite theorem. We also discuss weaker forms of non-manipulability and strategy-proofness. Comparing two frequently discussed aggregation rules, we show that “conclusion-based voting” is less vulnerable to manipulation (...) than “premise-based voting”, which is strategy-proof only for “reason-oriented” individuals. Surprisingly, for “outcome-oriented” individuals, the two rules are strategically equivalent, generating identical judgments in equilibrium. Our results introduce game-theoretic considerations into judgment aggregation and have implications for debates on deliberative democracy. (shrink)

This paper addresses the problem of judgment aggregation in science. How should scientists decide which propositions to assert in a collaborative document? We distinguish the question of what to write in a collaborative document from the question of collective belief. We argue that recent objections to the application of the formal literature on judgment aggregation to the problem of judgment aggregation in science apply to the latter, not the former question. The formal literature has (...) introduced various desiderata for an aggregation procedure. Proposition-wise majority voting emerges as a procedure that satisfies all desiderata which represent norms of science. An interesting consequence is that not all collaborating scientists need to endorse every proposition asserted in a collaborative document. (shrink)

In the emerging literature on judgment aggregation over logically connected proposi- tions, expert rights or liberal rights have not been investigated yet. A group making collective judgments may assign individual members or subgroups with expert know- ledge on, or particularly affected by, certain propositions the right to determine the collective judgment on those propositions. We identify a problem that generalizes Sen's 'liberal paradox'. Under plausible conditions, the assignment of rights to two or more individuals or subgroups is (...) inconsistent with the unanimity principle, whereby unanimously accepted propositions are collectively accepted. The inconsistency can be avoided if individual judgments or rights satisfy special conditions. (shrink)

The paper contains an overview of the most important results presented in the monograph of the author "Teorie Językow Syntaktycznie-Kategorialnych" ("Theories of Syntactically-Categorial Languages" (in Polish), PWN, Warszawa-Wrocław 1985. In the monograph four axiomatic systems of syntactically-categorial languages are presented. The first two refer to languages of expression-tokens. The others also takes into consideration languages of expression-types. Generally, syntactically-categorial languages are languages built in accordance with principles of the theory of syntactic categories introduced by S. Leśniewski [1929,1930]; they are (...) connected with- the Ajdukiewicz’s work [1935] which was a continuation of Leśniewski’s idea and further developed and popularized in the research on categorial grammars, by Y. Bar-Hillel [1950,1953,1964]. To assign a suitable syntactic category to each word of the vocabulary is the main idea of syntactically-categorial approach to language. Compound expressions are built from the words of the vocabulary and then a suitable syntactic-category is assigned to each of them. A language built in this way should be decidable, which means that there should exist an algorithm for deciding about each expression of it, whether it is well-formed or is syntactically connected . The traditional, originating from Husserl, understanding of the syntactic category confronts some difficulties. This notion is defined by abstraction using the concept of affiliation of two expressions to the same syntactic category. (shrink)

What is the relationship between degrees of belief and binary beliefs? Can the latter be expressed as a function of the former—a so-called “belief-binarization rule”—without running into difficulties such as the lottery paradox? We show that this problem can be usefully analyzed from the perspective of judgment-aggregation theory. Although some formal similarities between belief binarization and judgment aggregation have been noted before, the connection between the two problems has not yet been studied in full generality. In (...) this paper, we seek to fill this gap. The paper is organized around a baseline impossibility theorem, which we use to map out the space of possible solutions to the belief-binarization problem. Our theorem shows that, except in limiting cases, there exists no belief-binarization rule satisfying four initially plausible desiderata. Surprisingly, this result is a direct corollary of the judgment-aggregation variant of Arrow’s classic impossibility theorem in social choice theory. (shrink)

Judgment-aggregation theory has always focused on the attainment of rational collective judgments. But so far, rationality has been understood in static terms: as coherence of judgments at a given time, defined as consistency, completeness, and/or deductive closure. This paper asks whether collective judgments can be dynamically rational, so that they change rationally in response to new information. Formally, a judgment aggregation rule is dynamically rational with respect to a given revision operator if, whenever all individuals revise (...) their judgments in light of some information (a learnt proposition), then the new aggregate judgments are the old ones revised in light of this information, i.e., aggregation and revision commute. We prove an impossibility theorem: if the propositions on the agenda are non-trivially connected, no judgment aggregation rule with standard properties is dynamically rational with respect to any revision operator satisfying some basic conditions on revision. Our theorem is the dynamic-rationality counterpart of some well-known impossibility theorems for static rationality. We also explore how dynamic rationality might be achieved by relaxing some of the conditions on the aggregation rule and/or the revision operator. Notably, premise-based aggregation rules are dynamically rational with respect to so-called premise-based revision operators. (shrink)

This paper introduces the theory QST of quasets as a formal basis for the Nmatrices. The main aim is to construct a system of Nmatrices by substituting standard sets by quasets. Since QST is a conservative extension of ZFA (the Zermelo-Fraenkel set theory with Atoms), it is possible to obtain generalized Nmatrices (Q-Nmatrices). Since the original formulation of QST is not completely adequate for the developments we advance here, some possible amendments to the theory are also considered. One of the (...) most interesting traits of such an extension is the existence of complementary quasets which admit elements with undetermined membership. Such elements can be interpreted as quantum systems in superposed states. We also present a relationship of QST with the theory of Rough Sets RST, which grants the existence of models for SQT formed by rough sets. Some consequences of the given formalism for the relation of logical consequence are also analysed. (shrink)

Paul Cilliers has developed a novel post-structural approach to complexity that has influenced several writers contributing to the current complexity literature. Concomitantly however, Cilliers advocates for modelling complex systems using connectionist neural networks (rather than analytic, rule-based models). In this paper, I argue that it is dilemmic to simultaneously hold these two positions. Cilliers’ post-structural interpretation of complexity states that models of complex systems are always contextual and provisional; there is no exclusive model of complex systems. This sentiment however (...) appears at odds with Cilliers’ promotion of connectionist neural networks as the best way to model complex systems. The lesson is that those who currently follow Cilliers’ post-structural approach to complexity cannot also develop a preferred model of complex systems, and those who currently advocate for some preferred model of complex systems cannot adopt the post-structural approach to complexity without giving up the purported objectivity and/or superiority of their preferred model. (shrink)

In his _Being Known_ Peacocke sets himself the task of answering how we come to know about metaphysical necessities. He proposes a semantic principle-based conception consisting of, first, his Principles of Possibility which pro­vide necessary and sufficient conditions for a new concept 'admissibility', and second, characterizations of possibility and of necessity in terms of that new con­cept. I focus on one structural feature; viz. the recursive application involved in the specification of 'admissibility'. After sketching Peacocke’s proposal, I intro­duce a (...) fictional protagonist, Cautious Peacocke, whose coherence I claim shows that Peacocke s proposal cannot be made good. I conclude with the conjecture that similar failure will attend any such semantic-based attempts to ground the epistemology of metaphysical necessity. -/- Dans son livre intitulé Being Known, C. Peacocke se propose de repondre à la question de savoir comment nous en venons a connaitre des nécessités métaphysiques. Il développe une conception sémantique reposant sur des principes comprenant, d’une part, ses Principes de Possibilité — qui fournissent les conditions nécessaires et suffisantes pour un nouveau concept, « l’admissibilité » — et d’autre part des caractérisations de la possibilité et de la nécessité a l’aide de ce nouveau concept. Je me concentre sur une caractéristique structurelle, a savoir l’application récursive a l’œuvre dans la spécification de «l’admissibilité ». Apres avoir esquisse la proposition de Peacocke, j’introduis un personnage fictif, Peacocke-prudent. Je soutiens que la cohérence de ce personnage montre que la proposition de Peacocke ne peut pas être satisfaite. Je conclus en conjecturant qu’un échec similaire se présentera pour toutes les tentatives de fonder l’épistemologie de la nécessité métaphysique sur de telles bases semantiques. (shrink)

This paper is about knowledge construction in music listening. It argues for an experiential approach to music cognition, stressing the dynamic-vectorial field of meaning rather than the symbolic field. Starting from the conceptual framework of deixis and indexical devices, it elaborates on the concept of pointing as a heuristic guide for sense-making which allows the listener to conceive of perceptual elements in terms of salience, valence and semantical weight. As such, the act of (mental) pointing can be predicative, either (...) in a nominalistic or processual way, giving a description of the temporal evolution of a situation as against episodic nominalizations that refer to just one single instance of the process. The latter, especially, are characterized by distancing and polarization between the listener and the music, allowing him/her to deal with the music also at a level of mental imagery and to construct a mental or cognitive map of its unfolding. (shrink)

How can different individuals' probability functions on a given sigma-algebra of events be aggregated into a collective probability function? Classic approaches to this problem often require 'event-wise independence': the collective probability for each event should depend only on the individuals' probabilities for that event. In practice, however, some events may be 'basic' and others 'derivative', so that it makes sense first to aggregate the probabilities for the former and then to let these constrain the probabilities for the latter. We formalize (...) this idea by introducing a 'premise-based' approach to probabilistic opinion pooling, and show that, under a variety of assumptions, it leads to linear or neutral opinion pooling on the 'premises'. This paper is the second of two self-contained, but technically related companion papers inspired by binary judgment-aggregation theory. (shrink)

The paper defends a variant of the material implication approach to the meaning of conditional sentences against some arguments that are considered to be widely subscribed to and/or important in the philosophical, psychological and linguistic literature. These arguments are shown to be wrong, debatable, or to miss their aim if the truth conditions defining material implication are viewed as determining nothing but the denotation of conditional sentences and if the function of conditional sentences in deduction (logic) is focused on (...) rather than in inferencing (reasoning). It is shown that some ‘paradoxes of material implication’ are due to inconsistent premises of deductions introduced by semantic relations between clauses constituting the premises, a fact which does not invalidate the approach. Other ‘paradoxes’ are shown to arise because they are based on uninformative deductions, violating a basic pragmatic principle. In addition, the paper introduces the distinction between the set of possible states of a mental model of the actual world and of alternative worlds. It is argued that material implication determines the denotation of an indicative conditional as a subset of the former set and the denotation of a subjunctive conditional as a subset of the latter set, thus unifying these two types of conditionals. (shrink)

The question “what is an interpretation?” is often intertwined with the perhaps even harder question “what is a scientific theory?”. Given this proximity, we try to clarify the first question to acquire some ground for the latter. The quarrel between the syntactic and semantic conceptions of scientific theories occupied a large part of the scenario of the philosophy of science in the 20th century. For many authors, one of the two currents needed to be victorious. We endorse that (...) such debate, at least in the terms commonly expressed, can be misleading. We argue that the traditional notion of “interpretation” within the syntax/semantic debate is not the same as that of the debate concerning the interpretation of quantum mechanics. As much as the term is the same, the term “interpretation” as employed in quantum mechanics has its meaning beyond (pure) logic. Our main focus here lies on the formal aspects of the solutions to the measurement problem. There are many versions of quantum theory, many of them incompatible with each other. In order to encompass a wider variety of approaches to quantum theory, we propose a different one with an emphasis on pure formalism. This perspective has the intent of elucidating the role of each so-called “interpretation” of quantum mechanics, as well as the precise origin of the need to interpret it. (shrink)

This paper puts forward an argument for a systematic, technical approach to formulation in verbal interaction. I see this as a kind of expansion of Sacks’ membership categorization analysis, and as something that is not offered (at least not in a fully developed form) by sequential analysis, the currently dominant form of conversation analysis. In particular, I suggest a technique for the study of “occasioned semantics,” that is, the study of structures of meaningful expressions in actual occasions of conversation. (...) I propose that meaning and rhetoric be approached through consideration of various dimensions or operations or properties, including, but not limited to, contrast and co-categorization, generalization and specification, scaling, and marking. As illustration, I consider a variety of cases, focused on generalization and specification. The paper can be seen as a return to some classical concerns with meaning, as illuminated by more recent insights into indexicality, social action, and interaction in recorded talk. (shrink)

In this paper, I introduce the emerging theory of judgment aggregation as a framework for studying institutional design in social epistemology. When a group or collective organization is given an epistemic task, its performance may depend on its ‘aggregation procedure’, i.e. its mechanism for aggregating the group members’ individual beliefs or judgments into corresponding collective beliefs or judgments endorsed by the group as a whole. I argue that a group’s aggregation procedure plays an important role in (...) determining whether the group can meet two challenges: the ‘rationality challenge’ and the ‘knowledge challenge’. The rationality challenge arises when a group is required to endorse consistent beliefs or judgments; the knowledge challenge arises when the group’s beliefs or judgments are required to track certain truths. My discussion seeks to identify those properties of an aggregation procedure that affect a group’s success at meeting each of the two challenges. (shrink)

In this paper we discuss a new perspective on the syntax-semantics interface. Semantics, in this new set-up, is not ‘read off’ from Logical Forms as in mainstream approaches to generative grammar. Nor is it assigned to syntactic proofs using a Curry-Howard correspondence as in versions of the Lambek Calculus, or read off from f-structures using Linear Logic as in Lexical-Functional Grammar (LFG, Kaplan & Bresnan [9]). All such approaches are based on the idea that syntactic objects (trees, proofs, (...) fstructures) are somehow prior and that semantics must be parasitic on those syntactic objects. We challenge this idea and develop a grammar in which syntax and semantics are treated in a strictly parallel fashion. The grammar will have many ideas in common with the (converging) frameworks of categorial grammar and LFG, but its treatment of the syntax-semantics interface is radically different. Also, although the meaning component of the grammar is a version of Montague semantics and although there are obvious affinities between Montague’s conception of grammar and the work presented here, the grammar is not compositional, in the sense that composition of meaning need not follow surface structure. (shrink)

Research has indicated that microRNAs (miRNAs), a special class of non-coding RNAs (ncRNAs), can perform important roles in different biological and pathological processes. miRNAs’ functions are realized by regulating their respective target genes (targets). It is thus critical to identify and analyze miRNA-target interactions for a better understanding and delineation of miRNAs’ functions. However, conventional knowledge discovery and acquisition methods have many limitations. Fortunately, semantic technologies that are based on domain ontologies can render great assistance in this regard. In (...) our previous investigations, we developed a miRNA domain-specific application ontology, Ontology for MIcroRNA Target (OMIT), to provide the community with common data elements and data exchange standards in the miRNA research. This paper describes (1) our continuing efforts in the OMIT ontology development and (2) the application of the OMIT to enable a semantic approach for knowledge capture of miRNA-target interactions. (shrink)

It's widely accepted that social facts about an individual's linguistic community can affect both the reference of her words and the concepts those words express. Theorists sympathetic to the internalist tradition have sought to accommodate these social dependence phenomena without altering their core theoretical commitments by positing deferential reference-fixing criteria. In this paper, we sketch a different explanation of social dependence phenomena, according to which all concepts are individuated in part by causal-historical relations linking token elements of thought.