Embedding Non-Ground Logic Programs into Autoepistemic Logic for Knowledge Base Combination

In the context of the Semantic Web, several approaches to the combination of ontologies, given in terms of theories of classical first-order logic and rule bases, have been proposed. They either cast rules into classical logic or limit the interaction between rules and ontologies. Autoepistemic logic (AEL) is an attractive formalism which allows to overcome these limitations, by serving as a uniform host language to embed ontologies and nonmonotonic logic programs into it. For the latter, so far only the propositional setting has been considered. In this paper, we present three embeddings of normal and three embeddings of disjunctive non-ground logic programs under the stable model semantics into first-order AEL. While the embeddings all correspond with respect to objective ground atoms, differences arise when considering non-atomic formulas and combinations with first-order theories. We compare the embeddings with respect to stable expansions and autoepistemic consequences, considering the embeddings by themselves, as well as combinations with classical theories. Our results reveal differences and correspondences of the embeddings and provide useful guidance in the choice of a particular embedding for knowledge combination.Comment: 52 pages, submitte

Properties grounded in identity

The topic of this dissertation are essential properties. The aim is to give an explication of the concept of essential properties in terms of the concept of metaphysical grounding. Along the way, the author proves several new results about formal theories of metaphysical grounding and develops a new hyperintensional theory of properties. Chapter 1 is the introduction of the thesis in which the author motivates the problem of explicating the concept of essential properties and gives adequacy criteria for a successful explication tracing back to Carnap. The author discusses the orthodox explication of essential properties in terms of metaphysical necessity and Fine's objections to it. He goes on to develop a new ground-theoretic explication of essential properties in an informal way, where the basic idea is that a property is essential to an object if and only if the property is metaphysically grounded in the identity or haecceity of the object. The author argues informally that the new explication provides natural solutions to the problems raised by Fine and make it the goal for the rest of the dissertation to make the account formally precise. Chapter 2 focuses on a axiomatic theories of metaphysical grounding. In particular, the author develops a new formal approach to the relation of partial ground, i.e. the relation of one truth holding partially in virtue of another. The main novelty of the chapter is the use of a grounding predicate rather than an operator to formalize statements of (partial) ground. The author develops the new theory in formal detail as a first-order theory, proves its consistency, and shows that it's a conservative extension of the well-known theory of positive truth. Moreover, the author constructs a concrete model of the theory. Then, the author extends the framework with typed truth predicates, which allow us to make statements about the grounds and truth of statements about the truth of other sentences. Also this theory the author proves consistent and a conservative extension of the ramified theory of positive truth. A model construction extending the construction of the base theory is also given. Ultimately, the author discards the theory for the purpose of the dissertation, because of technical problems that arise when we try to develop a satisfactory explication of essential properties in the framework. The author leaves further development of the framework for future work and argues that further investigating could lead to interesting and fruitful discussion between formal theorists of truth and metaphysical theorists of grounding. Chapter 3 develops a logic of iterated ground, i.e. relations of ground between statements of ground, using the operator approach. The author first discusses certain conceptual distinctions in the context of metaphysical ground in general and iterated ground in particular. The author argues that different conceptions of iterated ground lead to different logics of iterated ground. He goes on to develop the logic of iterated ground based on the idea that if one truth is grounded in others, then it's these grounds that ground the statement of ground itself. This view traces back to remarks by de Rosset and Litland. The logic is developed in formal detail, both syntactically and semantically, and its formal properties are investigated. To conclude the chapter, the author discusses certain problems that arise when we're trying to prove a completeness result for the logic and sketches a way around them. In chapter 4, the author develops a new hyperintensional theory of properties, which can distinguish in natural, semantic terms between necessarily co-extensional but intuitively distinct properties. The theory is based on the idea that we can individuate properties by means of what the author calls "exemplification criteria" of an object for a property, roughly the states of affairs that if they obtain explain why the object has the property. The author develops this theory both formally and informally and discusses in detail how it achieves a natural distinction between necessarily co-extensional but intuitively distinct properties. Chapter 5 is the conclusion, where the author brings the results of chapter 3 and 4 to bear on the informal explication of essential properties in terms of metaphysical ground from the introduction. The author argues that together the iterated logic of ground from chapter 3 and the hyperintensional property theory of chapter 4 allow us to make the explication formally precise in a way that satisfies the adequacy criteria for a successful explication laid out by Carnap. The author concludes with a brief discussion of possible ways of extending the results of the dissertation in various ways

Another plan for negation

The paper  presents a plan for negation, proposing a paradigm shift from the Australian plan for negation,  leading to a family of contra-classical logics. The two main ideas are the following:  Instead of shifting points of evaluation (in a frame), shift the evaluated formula. Introduce an incompatibility set for every atomic formula, extended to any compound formula, and impose the condition on valuations that a formula evaluates to true iff all the formulas in its incompatibility set evaluate to false. Thus, atomic sentences are not independent in their truth-values.  The resulting negation, in addition to excluding the negated formula, provides a positive alternative to the negated formula. I  also present a sound and complete natural deduction proof systems for those logics. In addition, the kind of negation considered in this paper is shown to provide an innovative notion of grounding negation.  &nbsp

Iterative Robust Visual Grounding with Masked Reference based Centerpoint Supervision

Visual Grounding (VG) aims at localizing target objects from an image based on given expressions and has made significant progress with the development of detection and vision transformer. However, existing VG methods tend to generate false-alarm objects when presented with inaccurate or irrelevant descriptions, which commonly occur in practical applications. Moreover, existing methods fail to capture fine-grained features, accurate localization, and sufficient context comprehension from the whole image and textual descriptions. To address both issues, we propose an Iterative Robust Visual Grounding (IR-VG) framework with Masked Reference based Centerpoint Supervision (MRCS). The framework introduces iterative multi-level vision-language fusion (IMVF) for better alignment. We use MRCS to ahieve more accurate localization with point-wised feature supervision. Then, to improve the robustness of VG, we also present a multi-stage false-alarm sensitive decoder (MFSD) to prevent the generation of false-alarm objects when presented with inaccurate expressions. The proposed framework is evaluated on five regular VG datasets and two newly constructed robust VG datasets. Extensive experiments demonstrate that IR-VG achieves new state-of-the-art (SOTA) results, with improvements of 25\% and 10\% compared to existing SOTA approaches on the two newly proposed robust VG datasets. Moreover, the proposed framework is also verified effective on five regular VG datasets. Codes and models will be publicly at https://github.com/cv516Buaa/IR-VG

Applications of Intuitionistic Logic in Answer Set Programming

We present some applications of intermediate logics in the field of Answer Set Programming (ASP). A brief, but comprehensive introduction to the answer set semantics, intuitionistic and other intermediate logics is given. Some equivalence notions and their applications are discussed. Some results on intermediate logics are shown, and applied later to prove properties of answer sets. A characterization of answer sets for logic programs with nested expressions is provided in terms of intuitionistic provability, generalizing a recent result given by Pearce. It is known that the answer set semantics for logic programs with nested expressions may select non-minimal models. Minimal models can be very important in some applications, therefore we studied them; in particular we obtain a characterization, in terms of intuitionistic logic, of answer sets which are also minimal models. We show that the logic G3 characterizes the notion of strong equivalence between programs under the semantic induced by these models. Finally we discuss possible applications and consequences of our results. They clearly state interesting links between ASP and intermediate logics, which might bring research in these two areas together.Comment: 30 pages, Under consideration for publication in Theory and Practice of Logic Programmin

Type-free truth

This book is a contribution to the flourishing field of formal and philosophical work on truth and the semantic paradoxes. Our aim is to present several theories of truth, to investigate some of their model-theoretic, recursion-theoretic and proof-theoretic aspects, and to evaluate their philosophical significance. In Part I we first outline some motivations for studying formal theories of truth, fix some terminology, provide some background on Tarski’s and Kripke’s theories of truth, and then discuss the prospects of classical type-free truth. In Chapter 4 we discuss some minimal adequacy conditions on a satisfactory theory of truth based on the function that the truth predicate is intended to fulfil on the deflationist account. We cast doubt on the adequacy of some non-classical theories of truth and argue in favor of classical theories of truth. Part II is devoted to grounded truth. In chapter 5 we introduce a game-theoretic semantics for Kripke’s theory of truth. Strategies in these games can be interpreted as reference-graphs (or dependency-graphs) of the sentences in question. Using that framework, we give a graph-theoretic analysis of the Kripke-paradoxical sentences. In chapter 6 we provide simultaneous axiomatizations of groundedness and truth, and analyze the proof-theoretic strength of the resulting theories. These range from conservative extensions of Peano arithmetic to theories that have the full strength of the impredicative system ID1. Part III investigates the relationship between truth and set-theoretic comprehen- sion. In chapter 7 we canonically associate extensions of the truth predicate with Henkin-models of second-order arithmetic. This relationship will be employed to determine the recursion-theoretic complexity of several theories of grounded truth and to show the consistency of the latter with principles of generalized induction. In chapter 8 it is shown that the sets definable over the standard model of the Tarskian hierarchy are exactly the hyperarithmetical sets. Finally, we try to apply a certain solution to the set-theoretic paradoxes to the case of truth, namely Quine’s idea of stratification. This will yield classical disquotational theories that interpret full second-order arithmetic without set parameters, Z2- (chapter 9). We also indicate a method to recover the parameters. An appendix provides some background on ordinal notations, recursion theory and graph theory

Swahili conditional constructions in embodied Frames of Reference: Modeling semantics, pragmatics, and context-sensitivity in UML mental spaces

Studies of several languages, including Swahili [swa], suggest that realis (actual, realizable) and irrealis (unlikely, counterfactual) meanings vary along a scale (e.g., 0.0–1.0). T-values (True, False) and P-values (probability) account for this pattern. However, logic cannot describe or explain (a) epistemic stances toward beliefs, (b) deontic and dynamic stances toward states-of-being and actions, and (c) context-sensitivity in conditional interpretations. (a)–(b) are deictic properties (positions, distance) of ‘embodied’ Frames of Reference (FoRs)—space-time loci in which agents perceive and from which they contextually act (Rohrer 2007a, b). I argue that the embodied FoR describes and explains (a)–(c) better than T-values and P-values alone. In this cognitive-functional-descriptive study, I represent these embodied FoRs using Unified Modeling LanguageTM (UML) mental spaces in analyzing Swahili conditional constructions to show how necessary, sufficient, and contributing conditions obtain on the embodied FoR networks level.Swahili, conditional constructions, UML, mental spaces, Frames of Reference, epistemic stance, deontic stance, dynamic stance, context-sensitivity, non-monotonic logi

A Goal-Directed Implementation of Query Answering for Hybrid MKNF Knowledge Bases

Ontologies and rules are usually loosely coupled in knowledge representation formalisms. In fact, ontologies use open-world reasoning while the leading semantics for rules use non-monotonic, closed-world reasoning. One exception is the tightly-coupled framework of Minimal Knowledge and Negation as Failure (MKNF), which allows statements about individuals to be jointly derived via entailment from an ontology and inferences from rules. Nonetheless, the practical usefulness of MKNF has not always been clear, although recent work has formalized a general resolution-based method for querying MKNF when rules are taken to have the well-founded semantics, and the ontology is modeled by a general oracle. That work leaves open what algorithms should be used to relate the entailments of the ontology and the inferences of rules. In this paper we provide such algorithms, and describe the implementation of a query-driven system, CDF-Rules, for hybrid knowledge bases combining both (non-monotonic) rules under the well-founded semantics and a (monotonic) ontology, represented by a CDF Type-1 (ALQ) theory. To appear in Theory and Practice of Logic Programming (TPLP