Guarded Teams: The Horizontally Guarded Case

Team semantics admits reasoning about large sets of data, modelled by sets of assignments (called teams), with first-order syntax. This leads to high expressive power and complexity, particularly in the presence of atomic dependency properties for such data sets. It is therefore interesting to explore fragments and variants of logic with team semantics that permit model-theoretic tools and algorithmic methods to control this explosion in expressive power and complexity. We combine here the study of team semantics with the notion of guarded logics, which are well-understood in the case of classical Tarski semantics, and known to strike a good balance between expressive power and algorithmic manageability. In fact there are two strains of guardedness for teams. Horizontal guardedness requires the individual assignments of the team to be guarded in the usual sense of guarded logics. Vertical guardedness, on the other hand, posits an additional (or definable) hypergraph structure on relational structures in order to interpret a constraint on the component-wise variability of assignments within teams. In this paper we investigate the horizontally guarded case. We study horizontally guarded logics for teams and appropriate notions of guarded team bisimulation. In particular, we establish characterisation theorems that relate invariance under guarded team bisimulation with guarded team logics, but also with logics under classical Tarski semantics

Institutionalising Ontology-Based Semantic Integration

We address what is still a scarcity of general mathematical foundations for ontology-based semantic integration underlying current knowledge engineering methodologies in decentralised and distributed environments. After recalling the first-order ontology-based approach to semantic integration and a formalisation of ontological commitment, we propose a general theory that uses a syntax-and interpretation-independent formulation of language, ontology, and ontological commitment in terms of institutions. We claim that our formalisation generalises the intuitive notion of ontology-based semantic integration while retaining its basic insight, and we apply it for eliciting and hence comparing various increasingly complex notions of semantic integration and ontological commitment based on differing understandings of semantics

An algebraic approach to general aggregation theory: Propositional-attitude aggregators as MV-homomorphisms

This paper continues Dietrich and List's [2010] work on propositional-attitude aggregation theory, which is a generalised unification of the judgment-aggregation and probabilistic opinion-pooling literatures. We first propose an algebraic framework for an analysis of (many-valued) propositional-attitude aggregation problems. Then we shall show that systematic propositional-attitude aggregators can be viewed as homomorphisms in the category of C.C. Chang's [1958] MV-algebras. Since the 2-element Boolean algebra as well as the real unit interval can be endowed with an MV-algebra structure, we obtain as natural corollaries two famous theorems: Arrow's theorem for judgment aggregation as well as McConway's [1981] characterisation of linear opinion pools.propositional attitude aggregation, judgment aggregation, linear opinion pooling, Arrow's impossibility theorem, many-valued logic, MV-algebra, homomorphism, Arrow's impossibility theorem, functional equation

Social choice of convex risk measures through Arrovian aggregation of variational preferences

It is known that a combination of the Maccheroni-Marinacci-Rustichini (2006) axiomatisation of variational preferences with the Föllmer-Schied (2002,2004) representation theorem for concave monetary utility functionals provides an (individual) decision-theoretic foundation for convex risk measures. The present paper is devoted to collective decision making with regard to convex risk measures and addresses the existence problem for non-dictatorial aggregation functions of convex risk measures - in the guise of variational preferences - satisfying Arrow-type rationality axioms (weak universality, systematicity, Pareto principle). We prove an impossibility result for finite electorates, viz. a variational analogue of Arrow's impossibility theorem. For infinite electorates, the possibility of rational aggregation of variational preferences (i.e. convex risk measures) depends on a uniform continuity condition for the variational preference profiles: We shall prove variational analogues of both Campbell's impossibility theorem and Fishburn's possibility theorem. Methodologically, we adopt the model-theoretic approach to aggregation theory inspired by Lauwers-Van Liedekerke (1995). In an appendix, we apply the Dietrich-List (2010) analysis of logical aggregation based on majority voting to the problem of variational preference aggregation. The fruit is a possibility theorem, but at the cost of considerable and - at least at first sight - rather unnatural restrictions on the domain of the variational preference aggregator.variational preference representation, convex risk measure, multiple priors preferences, Arrow-type preference aggregation, judgment aggregation, abstract aggregation theory, model theory, first-order predicate logic, ultrafilter, ultraproduct

Indestructibility of Vopenka's Principle

We show that Vopenka's Principle and Vopenka cardinals are indestructible under reverse Easton forcing iterations of increasingly directed-closed partial orders, without the need for any preparatory forcing. As a consequence, we are able to prove the relative consistency of these large cardinal axioms with a variety of statements known to be independent of ZFC, such as the generalised continuum hypothesis, the existence of a definable well-order of the universe, and the existence of morasses at many cardinals.Comment: 15 pages, submitted to Israel Journal of Mathematic

W-types in setoids

W-types and their categorical analogue, initial algebras for polynomial endofunctors, are an important tool in predicative systems to replace transfinite recursion on well-orderings. Current arguments to obtain W-types in quotient completions rely on assumptions, like Uniqueness of Identity Proofs, or on constructions that involve recursion into a universe, that limit their applicability to a specific setting. We present an argument, verified in Coq, that instead uses dependent W-types in the underlying type theory to construct W-types in the setoid model. The immediate advantage is to have a proof more type-theoretic in flavour, which directly uses recursion on the underlying W-type to prove initiality. Furthermore, taking place in intensional type theory and not requiring any recursion into a universe, it may be generalised to various categorical quotient completions, with the aim of finding a uniform construction of extensional W-types.Comment: 17 pages, formalised in Coq; v2: added reference to formalisatio