Standpoint extensions of KR formalisms have been recently introduced to incorporate multi-perspective modelling and reasoning capabilities. In such modal extensions, the integration of conceptual modelling and perspective annotations can be more or less tight, with monodic standpoint extensions striking a good balance as they enable advanced modelling while preserving good reasoning complexities. We consider the extension of C² – the counting two-variable fragment of first-order logic – by monodic standpoints. At the core of our treatise is a polytime translation of formulae in said formalism into standpoint-free C², requiring elaborate model-theoretic arguments. By virtue of this translation, the NEXPTIME-complete complexity of checking satisfiability in C² carries over to our formalism. As our formalism subsumes monodic S5 over C², our result also significantly advances the state of the art in research on first-order modal logics. As a practical consequence, the very expressive description logics ?ℋ?ℐ?ℬs and ?ℛ?ℐ?ℬs which subsume the popular W3C-standardized OWL 1 and OWL 2 ontology languages, are shown to allow for monodic standpoint extensions without any increase of standard reasoning complexity. We prove that NEXPTIME-hardness already occurs in much less expressive DLs as long as they feature both nominals and monodic standpoints. We also show that, with inverses, functionality, and nominals present, minimally lifting the monodicity restriction leads to undecidability.

Standpoint logic is a recently proposed modal logic framework that is well-suited for multiperspective reasoning and ontology integration. For this reason, combinations of standpoint logic with description logics (DLs) are of special interest. Prior work has shown that it is possible to add standpoints to numerous decidable fragments of first-order logics - including very expressive DLs up to SROIQbs - while preserving their reasoning complexity, so long as standpoint modalities are limited to the axiom level. A more expressive tighter modal integration, where standpoint modalities are also allowed to occur in concept expressions, has so far only been investigated for the much less expressive DL EL+. In this paper, we push this line of research showing that the DL SHIQ allows for a tight modal integration with standpoints without compromising its ExpTime reasoning complexity. The core insight toward this result is that any satisfiable knowledge base admits a model with only polynomially many worlds, an argument which requires a rather elaborate model-theoretic construction. This allows us to establish a polynomial equisatisfiable translation into plain SHIQ which, beyond showing the theoretical result, enables us to use highly optimised OWL reasoners to provide practical reasoning support for ontology languages extended by standpoint modelling. We complement our findings with the observation that our techniques would fail upon adding the modelling feature of nominals to the underlying DL.

Standard first-order logic interprets reference, predication and quantification in terms of fixed denotations with respect to a domain of precise objects. We explore ways to generalise this semantics to account for variability of meaning due to factors such as vagueness, context and diversity of definitions or opinions. We present Variable Reference Logic (VRL), an elaboration of Standpoint Logic, which is a multi-modal logic based on a variety of Supervaluation Semantics. VRL can accommodate several modes of variability in relation to both predicates and objects. Its principal novelty is that its semantics incorporates a domain of indefinite individuals, whose precise properties (such as spatial extension) are not fully determinate. Each indefinite individual is associated with a set of precise entities corresponding to possible precise versions of the individual.

The tractability of the lightweight description logic EL has allowed for the construction of large and widely used ontologies that support semantic interoperability. However, comprehensive domains with a broad user base are often at odds with strong axiomatisations otherwise useful for inferencing, since these are usually context dependent and subject to diverging perspectives. In this paper we introduce Standpoint EL, a multi-modal extension of EL that allows for the integrated representation of domain knowledge relative to diverse, possibly conflicting standpoints (or contexts), which can be hierarchically organised and put in relation to each other. We establish that Standpoint EL still exhibits EL's favourable PTime standard reasoning, whereas introducing additional features like empty standpoints, rigid roles, and nominals makes standard reasoning tasks intractable.

Standpoint EL is a multi-modal extension of the popular description logic EL that allows for the integrated representation of domain knowledge relative to diverse standpoints or perspectives. Advantageously, its satisfiability problem has recently been shown to be in PTime, making it a promising framework for large-scale knowledge integration. In this paper, we show that we can further push the expressivity of this formalism, arriving at an extended logic, called Standpoint EL+, which allows for axiom negation, role chain axioms, self-loops, and other features, while maintaining tractability. This is achieved by designing a satisfiability-checking deduction calculus, which at the same time addresses the need for practical algorithms. We demonstrate the feasibility of our calculus by presenting a prototypical Datalog implementation of its deduction rules.

Many complex scenarios require the coordination of agents holding different points of view, possibly cooperating and not necessarily agreeing. For this reason, standpoint logic (SL) has been recently introduced in the context of knowledge integration, allowing one to reason with diverse and potentially conflicting viewpoints held by different agents. Linear temporal logic (LTL) is the most widely known formalism to express temporal properties of systems and processes, both in formal methods and artificial intelligence related fields. In this paper, we present 'standpoint linear temporal logic' (SLTL), a new logic that combines the temporal features of LTL with the multi-perspective modelling capacity of SL. We define the logic SLTL, its syntax, its semantics, establish its decidability and complexity, and provide a terminating tableau calculus to automate SLTL reasoning. Conveniently, this offers a clear path to extend existing LTL reasoners to provide practical reasoning support for temporal reasoning in multi-perspective settings.

Abstract The importance of taking individual, potentially conflicting perspectives into account when dealing with knowledge has been widely recognised. Many existing ontology management approaches fully merge knowledge perspectives, which may require weakening in order to maintain consistency; others represent the distinct views in an entirely detached way. As an alternative, we proposeStandpoint Logic, a simple, yet versatile multi-modal logic “add-on” for existing KR languages intended for the integrated representation of domain knowledge relative to diverse, possibly conflictingstandpoints, which can be hierarchically organised, combined, and put in relation with each other. Starting from the generic framework ofFirst-Order Standpoint Logic(FOSL), we subsequently focus our attention on the fragment ofsententialformulas, for which we provide a polytime translation into the standpoint-free version. This result yields decidability and favourable complexities for a variety of highly expressive decidable fragments of first-order logic. Using some elaborate encoding tricks, we then establish a similar translation for the very expressive description logic $$\mathcal {SROIQ}b_s$$ SROIQbs underlying the OWL 2 DL ontology language. By virtue of this result, existing highly optimised OWL reasoners can be used to provide practical reasoning support for ontology languages extended by standpoint modelling.

Ontologies and knowledge bases encode, to a certain extent, the standpoints or perspectives of their creators. As differences and conflicts between standpoints should be expected in multi-agent scenarios, this will pose challenges for shared creation and usage of knowledge sources. Our work pursues the idea that, in some cases, a framework that can handle diverse and possibly conflicting standpoints is more useful and versatile than forcing their unification, and avoids common compromises required for their merge. Moreover, in analogy to the notion of family resemblance concepts, we propose that a collection of standpoints can provide a simpler yet more faithful and nuanced representation of some domains. To this end, we present standpoint logic, a multi-modal framework that is suitable for expressing information with semantically heterogeneous vocabularies, where a standpoint is a partial and acceptable interpretation of the domain. Standpoints can be organised hierarchically and combined, and complex correspondences can be established between them. We provide a formal syntax and semantics, outline the complexity for the propositional case, and explore the representational capacities of the framework in relation to standard techniques in ontology integration, with some examples in the Bio-Ontology domain.

In previous work exploring how to automatically generate typicality measures for spatial prepositions in grounded settings, we considered a semantic model based on Prototype Theory and introduced a method for learning its parameters from data. However, though there is much to suggest that spatial prepositions exhibit polysemy, each term was treated as exhibiting a single sense. The ability for terms to represent distinct but related meanings is unexplored in the work on grounded semantics and referring expressions, where even homonymy is rarely considered. In this paper we address this problem by analysing the issue of reference using spatial language and examining how the polysemy exhibited by spatial prepositions can be incorporated into semantic models for situated dialogue. We support our approach on theoretical developments of Prototype Theory, which suggest that polysemy may be analysed in terms of radial categories, characterised by having several prototypicality centres. After providing a brief overview of polysemy in spatial language and a review of the related work, we define the Baseline Model and discuss how polysemy may be incorporated to improve it. We introduce a method of identifying polysemes based on `ideal meanings' and a modification of the `principled polysemy' framework. In order to compare polysemes and aid typicality judgements we then introduce a notion of `polyseme hierarchy'. Subsequently, we test the performance of the extended Polysemy Model by comparing it to the Baseline Model as well as a data-driven model of polysemy which we derive with a clustering algorithm. We conclude that our method for incorporating polysemy into the Baseline Model provides significant improvement. Finally, we analyse the properties and behaviour of the generated Polysemy Model, providing some insight into the improvement in performance, as well as justification for the given methods.

Many papers have considered the problem of how to define forest. However, as we shall illustrate, while most definitions capture some important aspects of what it means to be a forest, they almost invariably omit or are very vague regarding other aspects. In the current paper we address this issue, firstly by providing a definitional framework based on spatial and physical properties, within which one can make explicit the implicit variability of the natural language forest concept in terms of explicit parameters. Our framework explicitly differentiates between the functions of classification, individuation and demarcation that comprise the interpretation of predicative terms. Whereas ontologies have traditionally concentrated predominantly on classification, we argue that in many cases (especially in the case of geographic concepts) criteria for individuation (i.e. establishing how many distinct individual objects of a given type exist) and demarcation (establishing the boundary of an object) require separate attention, involve their own particular definitional issues and are affected by vagueness in different ways. We also describe a prototype Prolog system that illustrates how our framework can be implemented.

This paper aims to lay a foundation for a systematic study of mechanisms for construction of definitions within a formal theory, by investigating operators for incremental construction of definitions of new relations from an existing set of primitives and previously defined relations. To illustrate our method, we apply it to two of the best known relation sets studied in KRR: Allen's Interval Algebra and Region Connection Calculus. We also show that systematic exploration of definitional possibilities can yield interesting insights into relation sets that were originally defined in a more ad hoc way, and opens the possibility for discovering new vocabulary for extending or refining existing calculi or for developing completely new calculi.