Being Metaphysically Unsettled: Barnes and Williams on Metaphysical Indeterminacy and Vagueness

This chapter discusses the defence of metaphysical indeterminacy by Elizabeth Barnes and Robert Williams and discusses a classical and bivalent theory of such indeterminacy. Even if metaphysical indeterminacy arguably is intelligible, Barnes and Williams argue in favour of it being so and this faces important problems. As for classical logic and bivalence, the chapter problematizes what exactly is at issue in this debate. Can reality not be adequately described using different languages, some classical and some not? Moreover, it is argued that the classical and bivalent theory of Barnes and Williams does not avoid the problems that arise for rival theories

Interpretation of Natural-language Robot Instructions: Probabilistic Knowledge Representation, Learning, and Reasoning

A robot that can be simply told in natural language what to do -- this has been one of the ultimate long-standing goals in both Artificial Intelligence and Robotics research. In near-future applications, robotic assistants and companions will have to understand and perform commands such as set the table for dinner'', make pancakes for breakfast'', or cut the pizza into 8 pieces.'' Although such instructions are only vaguely formulated, complex sequences of sophisticated and accurate manipulation activities need to be carried out in order to accomplish the respective tasks. The acquisition of knowledge about how to perform these activities from huge collections of natural-language instructions from the Internet has garnered a lot of attention within the last decade. However, natural language is typically massively unspecific, incomplete, ambiguous and vague and thus requires powerful means for interpretation. This work presents PRAC -- Probabilistic Action Cores -- an interpreter for natural-language instructions which is able to resolve vagueness and ambiguity in natural language and infer missing information pieces that are required to render an instruction executable by a robot. To this end, PRAC formulates the problem of instruction interpretation as a reasoning problem in first-order probabilistic knowledge bases. In particular, the system uses Markov logic networks as a carrier formalism for encoding uncertain knowledge. A novel framework for reasoning about unmodeled symbolic concepts is introduced, which incorporates ontological knowledge from taxonomies and exploits semantically similar relational structures in a domain of discourse. The resulting reasoning framework thus enables more compact representations of knowledge and exhibits strong generalization performance when being learnt from very sparse data. Furthermore, a novel approach for completing directives is presented, which applies semantic analogical reasoning to transfer knowledge collected from thousands of natural-language instruction sheets to new situations. In addition, a cohesive processing pipeline is described that transforms vague and incomplete task formulations into sequences of formally specified robot plans. The system is connected to a plan executive that is able to execute the computed plans in a simulator. Experiments conducted in a publicly accessible, browser-based web interface showcase that PRAC is capable of closing the loop from natural-language instructions to their execution by a robot

Standpoint Logic: A Logic for Handling Semantic Variability, with Applications to Forestry Information

It is widely accepted that most natural language expressions do not have precise universally agreed definitions that fix their meanings. Except in the case of certain technical terminology, humans use terms in a variety of ways that are adapted to different contexts and perspectives. Hence, even when conversation participants share the same vocabulary and agree on fundamental taxonomic relationships (such as subsumption and mutual exclusivity), their view on the specific meaning of terms may differ significantly. Moreover, even individuals themselves may not hold permanent points of view, but rather adopt different semantics depending on the particular features of the situation and what they wish to communicate. In this thesis, we analyse logical and representational aspects of the semantic variability of natural language terms. In particular, we aim to provide a formal language adequate for reasoning in settings where different agents may adopt particular standpoints or perspectives, thereby narrowing the semantic variability of the vague language predicates in different ways. For that purpose, we present standpoint logic, a framework for interpreting languages in the presence of semantic variability. We build on supervaluationist accounts of vagueness, which explain linguistic indeterminacy in terms of a collection of possible interpretations of the terms of the language (precisifications). This is extended by adding the notion of standpoint, which intuitively corresponds to a particular point of view on how to interpret vague terminology, and may be taken by a person or institution in a relevant context. A standpoint is modelled by sets of precisifications compatible with that point of view and does not need to be fully precise. In this way, standpoint logic allows one to articulate finely grained and structured stipulations of the varieties of interpretation that can be given to a vague concept or a set of related concepts and also provides means to express relationships between different systems of interpretation. After the specification of precisifications and standpoints and the consideration of the relevant notions of truth and validity, a multi-modal logic language for describing standpoints is presented. The language includes a modal operator for each standpoint, such that \standb{s}\phi means that a proposition $\phi$ is unequivocally true according to the standpoint $s$ --- i.e.\ $\phi$ is true at all precisifications compatible with $s$. We provide the logic with a Kripke semantics and examine the characteristics of its intended models. Furthermore, we prove the soundness, completeness and decidability of standpoint logic with an underlying propositional language, and show that the satisfiability problem is NP-complete. We subsequently illustrate how this language can be used to represent logical properties and connections between alternative partial models of a domain and different accounts of the semantics of terms. As proof of concept, we explore the application of our formal framework to the domain of forestry, and in particular, we focus on the semantic variability of `forest'. In this scenario, the problematic arising of the assignation of different meanings has been repeatedly reported in the literature, and it is especially relevant in the context of the unprecedented scale of publicly available geographic data, where information and databases, even when ostensibly linked to ontologies, may present substantial semantic variation, which obstructs interoperability and confounds knowledge exchange

Metasemantics and fuzzy mathematics

The present thesis is an inquiry into the metasemantics of natural languages, with a particular focus on the philosophical motivations for countenancing degreed formal frameworks for both psychosemantics and truth-conditional semantics. Chapter 1 sets out to offer a bird's eye view of our overall research project and the key questions that we set out to address. Chapter 2 provides a self-contained overview of the main empirical findings in the cognitive science of concepts and categorisation. This scientific background is offered in light of the fact that most variants of psychologically-informed semantics see our network of concepts as providing the raw materials on which lexical and sentential meanings supervene. Consequently, the metaphysical study of internalistically-construed meanings and the empirical study of our mental categories are overlapping research projects. Chapter 3 closely investigates a selection of species of conceptual semantics, together with reasons for adopting or disavowing them. We note that our ultimate aim is not to defend these perspectives on the study of meaning, but to argue that the project of making them formally precise naturally invites the adoption of degreed mathematical frameworks (e.g. probabilistic or fuzzy). In Chapter 4, we switch to the orthodox framework of truth-conditional semantics, and we present the limitations of a philosophical position that we call "classicism about vagueness". In the process, we come up with an empirical hypothesis for the psychological pull of the inductive soritical premiss and we make an original objection against the epistemicist position, based on computability theory. Chapter 5 makes a different case for the adoption of degreed semantic frameworks, based on their (quasi-)superior treatments of the paradoxes of vagueness. Hence, the adoption of tools that allow for graded membership are well-motivated under both semantic internalism and semantic externalism. At the end of this chapter, we defend an unexplored view of vagueness that we call "practical fuzzicism". Chapter 6, viz. the final chapter, is a metamathematical enquiry into both the fuzzy model-theoretic semantics and the fuzzy Davidsonian semantics for formal languages of type-free truth in which precise truth-predications can be expressed

Talking about Forests: an Example of Sharing Information Expressed with Vague Terms

Most natural language terms do not have precise universally agreed definitions that fix their meanings. Even when conversation participants share the same vocabulary and agree on taxonomic relationships (such as subsumption and mutual exclusivity, which might be encoded in an ontology), they may differ greatly in the specific semantics they give to the terms. We illustrate this with the example of `forest', for which the problematic arising of the assignation of different meanings is repeatedly reported in the literature. This is especially the case in the context of an unprecedented scale of publicly available geographic data, where information and databases, even when tagged to ontologies, may present a substantial semantic variation, which challenges interoperability and knowledge exchange. Our research addresses the issue of conceptual vagueness in ontology by providing a framework based on supervaluation semantics that explicitly represents the semantic variability of a concept as a set of admissible precise interpretations. Moreover, we describe the tools that support the conceptual negotiation between an agent and the system, and the specification and reasoning within standpoints

What is the Value of Vagueness?

Classically, vagueness has been considered something bad. It leads to the Sorites paradox, borderline cases, and the (apparent) violation of the logical principle of bivalence. Nevertheless, there have always been scholars claiming that vagueness is also valuable. Many have pointed out that we could not communicate as successfully or efficiently as we do if we would not use vague language. Indeed, we often use vague terms when we could have used more precise ones instead. Many scholars (implicitly or explicitly) assume that we do so because their vagueness has a positive function. But how and in what sense can vagueness be said to have a function or value? This paper is an attempt to give an answer to this question. After clarifying the concepts of vagueness and value, it examines nine arguments for the value of vagueness, which have been discussed in the literature. The (negative) result of this examination is, however, that there is not much reason to believe that vagueness has a value or positive function at all because none of the arguments is conclusive. A tenth argument that has not been discussed so far seems most promising but rests on a solely strategic notion of function

THE INDETERMINATE PRESENT: AN ESSAY ON QUANTUM MECHANICS AND THE OPEN FUTURE

The dissertation is a defense of the following conditional claim: if there are objective collapses of the wavefunction, then the future is genuinely open. Although this is no radically new idea, the strategy I shall use to defend it is a new one. It proceeds in two main steps. First, building upon the recent literature on metaphysical indeterminacy in quantum mechanics, I argue for the view that systems in superposition have be interpreted as objectively indeterminate state of affairs. Second, I propose an alternative way to think of openness, according to which the future is open as of t, if and only if there is an indeterminate state of affair S at t, and S becomes determinate at t\u2019 (with t\u2019 later than t). To argue for the second step, I will give an analysis of the objective collapses of the wavefunction as the becoming determinate of previously indeterminate systems. Furthermore, in developing my arguments, I will also make some remarks concerning the ontology of objective collapse interpretations of quantum mechanics, the issue of whether metaphysical indeterminacy can be at some derivate level of reality, and the possibility of the openness of the future being an emergent phenomenon

A Survey of Probabilistic Reasoning in Justification Logic

Σε αυτήν τη διπλωματική εργασία μελετούμε την έννοια της επιχειρηματολογίας (justification), αναπαριστάμενη σε ένα λογικό φορμαλισμό. Μελετούμε την επιστημική / δοξαστική αναπαράσταση της justification logic, μίας επέκτασης της κλασικής λογικής (classical logic) με φόρμουλες της μορφής t:F, που μεταφράζονται ως "Το t είναι επιχείρημα που υποδεικνύει την αλήθεια της θέσης (ή την πίστη στη θέση) F.". Παρουσιάζουμε τις βασικές σημασιολογίες της justification logic, συνοδευόμενες από τα αντίστοιχα θεωρήματα ορθότητας και πληρότητας και αναλύουμε πώς εκλαμβάνει η κάθε μία την έννοια της επιχειρηματολογίας. Επίσης, αναλύουμε την έννοια τις επιχειρηματολογίας συνυφασμένη με την έννοια της αβεβαιότητας, παρουσιάζοντας τις θεμελιώδεις probabilistic justification logics. Διατυπώνουμε τις αντίστοιχες σημασιολογίες, μαζί με τα αντίστοιχα θεωρήματα ορθότητας και πληρότητας και εξετάζουμε πώς η κάθε μία λογική αντιλαμβάνεται την αβεβαιότητα στο πλαίσιο της επιχειρηματολογίας. Τέλος, μελετούμε μία νέα σημασιολογία που προτάθηκε και μελετήθηκε εκ των E. Lehmann και T. Studer τα τελευταία τρία χρόνια, ονόματι subset models. Ελέγχουμε πώς τα subset models θα μπορούσαν να συνδυαστούν με τη θεωρία πιθανοτήτων, στην προσπάθεια κατασκευής μίας πιθανοτικής λογικής που διαχωρίζει μεταξύ της αβεβαιότητας υπό το πρίσμα της πειστικότητας του επιχειρήματος, της αβεβαιότητας υπό το πρίσμα της αποδεικτικότητας της θέσης εκ του επιχειρήματος και τις αβεβαιότητας ισχύς της θέσης.In this thesis, we study the notion of justification, interpreted in a logical formalism. Specifically, we study the epistemic/doxastic interpretation of justification logic; i.e., an expansion of classical logic with formulae of the form t:F, which translate as "t is an evidence of the truth of F.". We present the basic semantics for justification logic, along with the corresponding theorems of soundness and completeness, and analyze how each one of them perceives the notion of justification. Moreover, we examine the notion of justification in relation to the notion of uncertainty, by presenting the fundamental probabilistic justification logics. We present the corresponding semantics, accompanied with the corresponding soundness and (sort of) completeness and we investigate how each one of these perceives the uncertainty in the context of justification. Last but not least, we define the subset models, a recent semantics for justification logic proposed and studied by E. Lehmann and T. Studer. We analyze the ontology of justification, as it is expressed in this framework, and we examine how subset models could probably combine with the notion of uncertainty, in a way that distinguishes between the suasiveness of the evidence t, the conclusiveness of evidence t over assertion F, and the certainty of F