To be or not to be: Examining the Role of Language in a Concept of Negation

Negation is a complex, abstract concept, despite the ubiquity of words like “no” and “not” in even young children’s speech. One challenging aspect to words like “no” and “not” is that these words can serve many functions in speech, giving us tools to express an array of concepts such as denial, refusal, and nonexistence. Is there a single concept of “negation” that unites these separate negative functions – and if so, does understanding this concept require the structure of human language? In this paper we present a study demonstrating that adults spontaneously identify a concept of negation in the absence of explicit verbal instructions, even when the exemplars of negation are perceptually varied and represent many different functions of negation. Furthermore, tying up participants’ language ability using verbal shadowing impairs participants’ ability to identify a concept of negation, but does not impair participants’ ability to identify an equally complex control concept (natural kinds). We discuss our findings in light of theories regarding the representation of negation and the relationship between language and thought

Negation 'presupposition' and metarepresentation: a response to Noel Burton-Roberts

Metalinguistic negation (MN) is interesting for at least the following two reasons: (a) it is one instance of the much broader, very widespread and various phenomenon of metarepresentational use in linguistic communication, whose semantic and pragmatic properties are currently being extensively explored by both linguists and philosophers of language; (b) it plays a central role in recent accounts of presupposition-denial cases, such as ‘The king of France is not bald; there is no king of France’. It is this latter employment that discussion of metalinguistic negation has focused on since Horn (1985)'s key article on the subject. While Burton-Roberts (1989a, 1989b) saw the MN account of presupposition-denials as providing strong support for his semantic theory of presupposition, I have offered a multi-layered pragmatic account of these cases, which also involves MN, but maintains the view that the phenomenon of presupposition is pragmatic (Carston 1994, 1996, 1998a)

Reason Maintenance - Conceptual Framework

This paper describes the conceptual framework for reason maintenance developed as part of WP2

Knowledge Representation Concepts for Automated SLA Management

Outsourcing of complex IT infrastructure to IT service providers has increased substantially during the past years. IT service providers must be able to fulfil their service-quality commitments based upon predefined Service Level Agreements (SLAs) with the service customer. They need to manage, execute and maintain thousands of SLAs for different customers and different types of services, which needs new levels of flexibility and automation not available with the current technology. The complexity of contractual logic in SLAs requires new forms of knowledge representation to automatically draw inferences and execute contractual agreements. A logic-based approach provides several advantages including automated rule chaining allowing for compact knowledge representation as well as flexibility to adapt to rapidly changing business requirements. We suggest adequate logical formalisms for representation and enforcement of SLA rules and describe a proof-of-concept implementation. The article describes selected formalisms of the ContractLog KR and their adequacy for automated SLA management and presents results of experiments to demonstrate flexibility and scalability of the approach.Comment: Paschke, A. and Bichler, M.: Knowledge Representation Concepts for Automated SLA Management, Int. Journal of Decision Support Systems (DSS), submitted 19th March 200

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

Report on the EHCR (Deliverable 26.2)

This deliverable is the second for Workpackage 26. The first, submitted after Month 12, summarised the areas of research that the partners had identified as being relevant to the semantic indexing of the EHR. This second one reports progress on the key threads of work identified by the partners during the project to contribute towards semantically interoperable and processable EHRs. This report provides a set of short summaries on key topics that have emerged as important, and to which the partners are able to make strong contributions. Some of these are also being extended via two new EU Framework 6 proposals that include WP26 partners: this is also a measure of the success of this Network of Excellence

Quantum Structure of Negation and Conjunction in Human Thought

We analyse in this paper the data collected in a set of experiments performed on human subjects on the combination of natural concepts. We investigate the mutual influence of conceptual conjunction and negation by measuring the membership weights of a list of exemplars with respect to two concepts, e.g., 'Fruits' and 'Vegetables', and their conjunction 'Fruits And Vegetables', but also their conjunction when one or both concepts are negated, namely, 'Fruits And Not Vegetables', 'Not Fruits And Vegetables' and 'Not Fruits And Not Vegetables'. Our findings sharpen existing analysis on conceptual combinations, revealing systematic and remarkable deviations from classical (fuzzy set) logic and probability theory. And, more important, our results give further considerable evidence to the validity of our quantum-theoretic framework for the combination of two concepts. Indeed, the representation of conceptual negation naturally arises from the general assumptions of our two-sector Fock space model, and this representation faithfully agrees with the collected data. In addition, we find a further significant deviation and a priori unexpected from classicality, which can exactly be explained by assuming that human reasoning is the superposition of an 'emergent reasoning' and a 'logical reasoning', and that these two processes can be successfully represented in a Fock space algebraic structure.Comment: 44 pages. arXiv admin note: text overlap with arXiv:1406.235

Some Logical Notations for Pragmatic Assertions

The pragmatic notion of assertion has an important inferential role in logic. There are also many notational forms to express assertions in logical systems. This paper reviews, compares and analyses languages with signs for assertions, including explicit signs such as Frege’s and Dalla Pozza’s logical systems and implicit signs with no specific sign for assertion, such as Peirce’s algebraic and graphical logics and the recent modification of the latter termed Assertive Graphs. We identify and discuss the main ‘points’ of these notations on the logical representation of assertions, and evaluate their systems from the perspective of the philosophy of logical notations. Pragmatic assertions turn out to be useful in providing intended interpretations of a variety of logical systems

On computing the determinant, other characteristic polynomial coefficients, and inverse in Clifford algebras of arbitrary dimension

In this paper, we solve the problem of computing the inverse in Clifford algebras of arbitrary dimension. We present basis-free formulas of different types (explicit and recursive) for the determinant, other characteristic polynomial coefficients, adjugate, and inverse in real Clifford algebras (or geometric algebras) over vector spaces of arbitrary dimension $n$. The formulas involve only the operations of multiplication, summation, and operations of conjugation without explicit use of matrix representation. We use methods of Clifford algebras (including the method of quaternion typification proposed by the author in previous papers and the method of operations of conjugation of special type presented in this paper) and generalizations of numerical methods of matrix theory (the Faddeev-LeVerrier algorithm based on the Cayley-Hamilton theorem; the method of calculating the characteristic polynomial coefficients using Bell polynomials) to the case of Clifford algebras in this paper. We present the construction of operations of conjugation of special type and study relations between these operations and the projection operations onto fixed subspaces of Clifford algebras. We use this construction in the analytical proof of formulas for the determinant, other characteristic polynomial coefficients, adjugate, and inverse in Clifford algebras. The basis-free formulas for the inverse give us basis-free solutions to linear algebraic equations, which are widely used in computer science, image and signal processing, physics, engineering, control theory, etc. The results of this paper can be used in symbolic computation.Comment: 24 page