Substructural Logics in Natural Deduction

Extensions of Natural Deduction to Substructural Logics of IntuitionisticLogic are shown: Fragments of Intuitionistic Linear, Relevantand BCK Logic. Rules for implication, conjunction, disjunctionand falsum are defined, where conjunction and disjunction respectcontexts of assumptions. So, conjunction and disjunction areadditive in the terminology of linear logic. Explicit contractionand weakening rules are given. It is shown that conversionsand permutations can be adapted to all these rules, and thatweak normalisation and subformula property holds. The resultsgeneralise to quantification.     

Ontologies and Construals in Lexical Semantics

The purpose of this paper is to propose a framework of lexical meaning, broadly along the lines of Cognitive Semantics (Langacker 1987a). Within the proposed model, all aspects of meaning are to be explained in terms of properties of ontologies in conceptual space, i.e. properties of content ontologies and schematic ontologies and construals which are imposed on the conceptual structures on the occasion of use. It is through the operations of construals on ontological structures that different readings of lexical expressions arise. Lexical meanings are dynamic and sensitive to contextual demands, rather than fixed and stable. In a dynamic, usage-based model like this, polysemy and multiple readings emerge as a natural consequence of the human ability to think flexibly. Another more specific purpose of this paper is to draw attention to the usefulness of ontologies in linguistic research in general and semantic modelling in particular.     

现象学与逻辑学

无论在胡塞尔思想中还是在海德格尔思想中,现象学与逻辑学的关系都构成一个核心问题。本文首先再现了胡塞尔前后期在此问题上的相关研究,并指出他的超越论逻辑学的要点在于对本质的前逻辑直观,也是最有可能为逻辑学提供哲学支撑的因素。其次,在海德格尔方面,根据律概念成为讨论现象学与逻辑学关系的切入点,由此导出他的“存在理解”、“无蔽”和“自由”的概念解释。他们的共同点在于：把形式逻辑看作陈述逻辑,并试图用前谓词判断的哲学逻辑学来为它奠基。     

Second order inductive logic and Wilmers' principle

We extend the framework of Inductive Logic to Second Order languages and introduce Wilmers' Principle, a rational principle for probability functions on Second Order languages. We derive a representation theorem for functions satisfying this principle and investigate its relationship with the first order principles of Regularity and Super Regularity.     

Proof Nets for the Multimodal Lambek Calculus

We present a novel way of using proof nets for the multimodal Lambek calculus, which provides a general treatment of both the unary and binary connectives. We also introduce a correctness criterion which is valid for a large class of structural rules and prove basic soundness, completeness and cut elimination results. Finally, we will present a correctness criterion for the original Lambek calculus Las an instance of our general correctness criterion.     

Disjunctive logic programming with types and objects: The DLV system

The paper presents DLV⁺, a Disjunctive Logic Programming (DLP) system with object-oriented constructs, including classes, objects, (multiple) inheritance, and types. DLV⁺ is built on top of DLV (a state-of-the art DLP system), and provides a graphical user interface that allows one to specify, update, browse, query, and reason on knowledge bases. Two strong points of the system are the powerful type-checking mechanism and the advanced interface for visual querying.DLV⁺ is already used for the development of knowledge based applications for information extraction and text classification.     

Ontologies and Worlds in Category Theory: Implications for Neural Systems

We propose category theory, the mathematical theory of structure, as a vehicle for defining ontologies in an unambiguous language with analytical and constructive features. Specifically, we apply categorical logic and model theory, based upon viewing an ontology as a sub-category of a category of theories expressed in a formal logic. In addition to providing mathematical rigor, this approach has several advantages. It allows the incremental analysis of ontologies by basing them in an interconnected hierarchy of theories, with an operation on the hierarchy that expresses the formation of complex theories from simple theories that express first principles. Another operation forms abstractions expressing the shared concepts in an array of theories. The use of categorical model theory makes possible the incremental analysis of possible worlds, or instances, for the theories, and the mapping of instances of a theory to instances of its more abstract parts. We describe the theoretical approach by applying it to the semantics of neural networks.     

试论"真矛盾"及次协调逻辑的哲学价值

二十世纪后期以来,再也没有哪一种逻辑像次协调逻辑那样,在取得丰富研究成果的同时,也领略到了极为尖锐的批判,仿佛其本身就是一种意味深长的“矛盾”。依照次协调逻辑“真矛盾”的观点所构建的次协调逻辑系统,夷非所思地试图要容纳我们所认知的悖论、辩证矛盾、甚至逻辑矛盾。次协调逻辑试图要和悖论永久共存,但我们可以为了暂时的搁置这种矛盾,发展某理论的其他方面而接受这种逻辑技术。次协调逻辑在反映人脑的容错机制上具有重要的描述功能,这对提高计算机的智能化具有十分重要的实践意义。     

A logic of intention and attempt

We present a modal logic called (logic of intention and attempt) in which we can reason about intention dynamics and intentional action execution. By exploiting the expressive power of , we provide a formal analysis of the relation between intention and action and highlight the pivotal role of attempt in action execution. Besides, we deal with the problems of instrumental reasoning and intention persistence.     

Modal Deduction in Second-Order Logic and Set Theory - II

In this paper, we generalize the set-theoretic translation method for poly-modal logic introduced in [11] to extended modal logics. Instead of devising an ad-hoc translation for each logic, we develop a general framework within which a number of extended modal logics can be dealt with. We first extend the basic set-theoretic translation method to weak monadic second-order logic through a suitable change in the underlying set theory that connects up in interesting ways with constructibility; then, we show how to tailor such a translation to work with specific cases of extended modal logics.     

Propositional Plausible Logic: Introduction and Implementation

Plausible Logic allows defeasible deduction with arbitrary propositions, and yet when sufficiently simplified it is very similar to the Defeasible Logics of Billington and Nute. This paper presents Plausible Logic, explains some of the ideas behind the definitions, applies Plausible Logic to an example, and proves a coherence result which indicates that Plausible Logic is well behaved. We also report the first complete implementation of propositional Plausible Logic. The implementation has a web interface which makes it available to researchers and students everywhere. The implementation is evaluated experimentally, and is shown to be capable of handling tens of thousands of rules and sufficiently many disjunctions for realistic problems.     

Formal and Applied Counseling in Israel

Living in Israel is intensive and demanding but also meaningful and exciting. This article addresses the gap between the narrowly defined formal status of counseling in Israel and the widespread occurrence of counseling in various settings. It is argued that several recent changes, especially in the definition of treatment, along with the increasing need for counseling, especially in minority ethnic groups, set the stage for optimism regarding the future of counseling in Israel.     

Cogex: A semantically and contextually enriched logic prover for question answering

This paper presents the architecture and functionality of a logic prover designed for question answering. The approach transforms questions and answer passages into logic representations based on syntactic, semantic and contextual information. World knowledge supplements the linguistic, ontological, and temporal axioms supplied to the prover which renders a deep understanding of the relationship between the question and answer text. The trace of the proofs provides a basis for generating human comprehensible answer justifications. The results show that the prover boosts the performance of the Question Answering system on TREC 2004 questions by 12%.     

Shortcuts and Dynamic Marking in the Tableau Method for Adaptive Logics

Adaptive logics typically pertain to reasoning procedures for which there is no positive test. In [7], we presented a tableau method for two inconsistency-adaptive logics. In the present paper, we describe these methods and present several ways to increase their efficiency. This culminates in a dynamic marking procedure that indicates which branches have to be extended first, and thus guides one towards a decision — the conclusion follows or does not follow — in a very economical way.     

The Relation between Formal and Informal Logic

The issue of the relationship between formal and informal logic depends strongly on how one understands these two designations. While there is very little disagreement about the nature of formal logic, the same is not true regarding informal logic, which is understood in various (often incompatible) ways by various thinkers. After reviewing some of the more prominent conceptions of informal logic, I will present my own, defend it and then show how informal logic, so understood, is complementary to formal logic.