An institution theory of formal meta-modelling in graphically extended BNF

Meta-modelling plays an important role in model driven software development. In this paper, a graphic extension of BNF (GEBNF) is proposed to define the abstract syntax of graphic modelling languages. From a GEBNF syntax definition, a formal predicate logic language can be induced so that meta-modelling can be performed formally by specifying a predicate on the domain of syntactically valid models. In this paper, we investigate the theoretical foundation of this metamodelling approach. We formally define the semantics of GEBNF and its induced predicate logic languages, then apply Goguen and Burstall’s institution theory to prove that they form a sound and valid formal specification language for meta-modelling

Everything, and then some

On its intended interpretation, logical, mathematical and metaphysical discourse sometimes seems to involve absolutely unrestricted quantification. Yet our standard semantic theories do not allow for interpretations of a language as expressing absolute generality. A prominent strategy for defending absolute generality, influentially proposed by Timothy Williamson in his paper ‘Everything’ (2003), avails itself of a hierarchy of quantifiers of ever increasing orders to develop non-standard semantic theories that do provide for such interpretations. However, as emphasized by Øystein Linnebo and Agustín Rayo (2012), there is pressure on this view to extend the quantificational hierarchy beyond the finite level, and, relatedly, to allow for a cumulative conception of the hierarchy. In his recent book, Modal Logic as Metaphysics (2013), Williamson yields to that pressure. I show that the emerging cumulative higher-orderist theory has implications of a strongly generality-relativist flavour, and consequently undermines much of the spirit of generality absolutism that Williamson set out to defend

Constrained Query Answering

Traditional answering methods evaluate queries only against positive and definite knowledge expressed by means of facts and deduction rules. They do not make use of negative, disjunctive or existential information. Negative or indefinite knowledge is however often available in knowledge base systems, either as design requirements, or as observed properties. Such knowledge can serve to rule out unproductive subexpressions during query answering. In this article, we propose an approach for constraining any conventional query answering procedure with general, possibly negative or indefinite formulas, so as to discard impossible cases and to avoid redundant evaluations. This approach does not impose additional conditions on the positive and definite knowledge, nor does it assume any particular semantics for negation. It adopts that of the conventional query answering procedure it constrains. This is achieved by relying on meta-interpretation for specifying the constraining process. The soundness, completeness, and termination of the underlying query answering procedure are not compromised. Constrained query answering can be applied for answering queries more efficiently as well as for generating more informative, intensional answers

Computing Preferred Answer Sets by Meta-Interpretation in Answer Set Programming

Most recently, Answer Set Programming (ASP) is attracting interest as a new paradigm for problem solving. An important aspect which needs to be supported is the handling of preferences between rules, for which several approaches have been presented. In this paper, we consider the problem of implementing preference handling approaches by means of meta-interpreters in Answer Set Programming. In particular, we consider the preferred answer set approaches by Brewka and Eiter, by Delgrande, Schaub and Tompits, and by Wang, Zhou and Lin. We present suitable meta-interpreters for these semantics using DLV, which is an efficient engine for ASP. Moreover, we also present a meta-interpreter for the weakly preferred answer set approach by Brewka and Eiter, which uses the weak constraint feature of DLV as a tool for expressing and solving an underlying optimization problem. We also consider advanced meta-interpreters, which make use of graph-based characterizations and often allow for more efficient computations. Our approach shows the suitability of ASP in general and of DLV in particular for fast prototyping. This can be fruitfully exploited for experimenting with new languages and knowledge-representation formalisms.Comment: 34 pages, appeared as a Technical Report at KBS of the Vienna University of Technology, see http://www.kr.tuwien.ac.at/research/reports

Semantic values in higher-order semantics

Recently, some philosophers have argued that we should take quantification of any (finite) order to be a legitimate and irreducible, sui generis kind of quantification. In particular, they hold that a semantic theory for higher-order quantification must itself be couched in higher-order terms. Øystein Linnebo has criticized such views on the grounds that they are committed to general claims about the semantic values of expressions that are by their own lights inexpressible. I show that Linnebo's objection rests on the assumption of a notion of semantic value or contribution which both applies to expressions of any order, and picks out, for each expression, an extra-linguistic correlate of that expression. I go on to argue that higher-orderists can plausibly reject this assumption, by means of a hierarchy of notions they can use to describe the extra-lingustic correlates of expressions of different orders