Deduction Rules Research Articles

A temporal-probabilistic database model for information extraction

Temporal annotations of facts are a key component both for building a high-accuracy knowledge base and for answering queries over the resulting temporal knowledge base with high precision and recall. In this paper, we present a temporal-probabilistic database model for cleaning uncertain temporal facts obtained from information extraction methods. Specifically, we consider a combination of temporal deduction rules, temporal consistency constraints and probabilistic inference based on the common possible-worlds semantics with data lineage, and we study the theoretical properties of this data model. We further develop a query engine which is capable of scaling to very large temporal knowledge bases, with nearly interactive query response times over millions of uncertain facts and hundreds of thousands of grounded rules. Our experiments over two real-world datasets demonstrate the increased robustness of our approach compared to related techniques based on constraint solving via Integer Linear Programming (ILP) and probabilistic inference via Markov Logic Networks (MLNs). We are also able to show that our runtime performance is more than competitive to current ILP solvers and the fastest available, probabilistic but non-temporal, database engines.

A natural deduction system for bundled branching time logic

We introduce a natural deduction system for the until-free subsystem of the branching time logic Although we work with labelled formulas, our system differs conceptually from the usual labelled deduction systems because we have no relational formulas. Moreover, no deduction rule embodies semantic features such as properties of accessibility relation or similar algebraic properties. We provide a suitable semantics for our system and prove that it is sound and weakly complete with respect to such semantics.

Ontology Fusion in High-Level-Architecture-Based Collaborative Engineering Environments

In high-level-architecture (HLA)-based distributed heterogeneous collaborative engineering environments (CEEs), the construction of federation object model files is time consuming. This paper presents an ontology fusion approach aiming at establishing a common understanding in such collaborative environments. The proposed approach has three steps: ontology mapping, ontology alignment, and ontology merging. Ontology mapping employs a top-down approach to explore all bridge relations between two terms from different ontologies based on bridge axioms and deduction rules. Ontology alignment adopts a bottom-up approach to discover implicit bridge relations between two terms from different domain ontologies based on equivalent inference. Ontology merging generates a new collaboration ontology from discovered equivalent bridge relations. It adopts an axiom-based ontology fusion strategy and takes heavy-weighted ontologies into consideration. It can find all the explicit and derived interontology relations. In a typical CEE, the proposed approach has a great potential to improve the efficiency of preparation for HLA-based collaborative engineering processes, reduce the work load for adaptive adjustment of existing platforms, and enhance the reusability and flexibility of CEEs. A case study has been conducted to validate the feasibility of the proposed approach.

An intelligent task analysis approach for special education based on MIRA

This paper describes a novel approach for generating a logical sequence of tasks in the task analysis process of special education. This approach is based on the formalism MIRA (Mīmāṁsā Inspired Representation of Actions), which has the feature of expressing an action as reason, instruction and goal. MIRA also prescribes a set of deduction rules, which helps in the reasoning process of actions. These features are incorporated in this approach and a software tool, namely MIRATaskGen is designed, which facilitates the task analysis process of special education. The software receives various action related inputs along with the start and finish stages and generates a sequence of tasks from the start to the finish. This tool also informs the user, whether the desired goal can be achieved. If the desired goal cannot be achieved, then the sequence of actions from the start to a point of discontinuity is detected.

Failures of Categoricity and Compositionality for Intuitionistic Disjunction

There are at least two reasonable types of logical inferentialism. The first type of inferentialism views the meaning of a connective in proof-theoretic terms, having no truck with ordinary model theory except in its role as an instrument to illuminate various proof-theoretic features of a connective. The second type of inferentialism is more modest, allowing that we have some prior conception of the meaning that the natural deduction rules for a particular connective determine. Such a position would look to the conditions forced by acceptance of a set of rules against a background model theory for an account of connective meaning. This position is moderate, plausible, and problematic. In the case of classical logic, against the presumption of standard extensional semantics, Carnap long ago demonstrated the general failure of proof-rules to induce the intended boolean interpretation of the connectives. There have been a number of attempts to solve this problem by modifying the natural deduction format, but none have achieved anything like a consensus.

MP-CLOSED SUBSETS IN BASIC ALGEBRAS

A subset M of a given basic algebra [Formula: see text] is MP-closed if a ∈ M and a → b ∈ M always imply b ∈ M for b ≤ a. We get a characterization of MP-closed subsets for commutative basic algebras in terms of closedness in the derived operation ⊙. If, moreover, the basic algebra is a chain, then a particular simple condition is derived. For basic algebras which are not commutative we derive only a closedness with respect to the deduction rule Modus Tollens.

On Coliva’s Judgmental Hinges

Annalisa Coliva's Moore and Wittgenstein: Scepticism, Certainty, and Common Sense does On Certainty, and Wittgenstein generally, a great service: it is the first in-depth study of Moore and Wittgenstein that places On Certainty within current epistemology. By this I mean, that it discusses its content, reception and repercussions in the technical terms of current epistemology and in the midst of current epistemologists. But it also manages to do this without losing the non-specialist reader to the often bewildering jargon of epistemology, and without viewing hinge certainty as an epistemic certainty. There is much that I agree with in Coliva’s reading of On Certainty, but her view of hinges as both judgments and norms seems to me to go against the spirit and the letter of On Certainty. In what follows, I will be mainly concerned with that view, but will conclude by adding a few words on Coliva's rejection of foundationalism in On Certainty. In her Introduction, Coliva refers to my classification of the main four 'readings' of On Certainty: the framework; the transcendental; the epistemic; and the therapeutic readings1, and situates herself as a framework reader, but with a difference. She agrees that Wittgenstein takes hinge certainties to be rules rather than empirical propositions, and that they are therefore not truth-evaluable (2010, 6-7), but she finds this problematic: to say that 'Here is my hand' is neither true nor false when I'm holding it in front of my eyes in optimal cognitive circumstances sounds 'extremely weird', and some hinges, such as 'Nobody's ever been on the moon appear false to us' (2010, 7-8). The weirdness felt by Coliva is reminiscent of Moore’s discomfort upon hearing Wittgenstein's 'puzzling assertion that 3+3=6 (and all rules of deduction, similarly) is neither true nor false' (MWL 73, 80). But Wittgenstein himself warned that this would be ‘apt to give an uncomfortable feeling’ (MWL 73). Wittgenstein’s point in barring truth-evaluability from grammatical rules, of which mathematical ones2, is to insist on their normative (as opposed to descriptive or evaluative) status: '3+3=6 is a rule as to the way we are going to talk ... it is a preparation for a description' (MWL 72). So that grammatical rules (or as Coliva prefers to call them: meaning constitutive rules) can be said to be preparation for, or antecedent to judgment, rather than themselves (expressions/instances of) judgments. However – perhaps because of the 'weirdness' in saying that 'Here is my hand' is not true as I'm holding it in front of my eyes in

Fuzzy decision implications

The aim of this paper is to provide the semantical and syntactical characteristics of fuzzy decision implications, an expression concerning two systems of fuzzy-sets. This Pavelka-style fuzzy logic starts from a fuzzy set of fuzzy decision implications and makes deductions from partially true decision implications. Following this idea, in semantical aspect, we present some basic results concerning completeness and more importantly, introduce the notion of “unite closure”, which is in fact important not only in semantical aspect but also in syntactical aspect. Besides, we derive three deduction rules, namely (F-Transformation), (F-Add) and (F-Sh↑) for syntactical aspect of fuzzy decision implications, which are proved to be sound and complete with respect to semantical aspect. The result ensures that one can obtain a closed fuzzy set of fuzzy decision implications by the semantical way or by the syntactical way, i.e., by the three deduction rules.

A New–old Characterisation of Logical Knowledge

We seek means of distinguishing logical knowledge from other kinds of knowledge, especially mathematics. The attempt is restricted to classical two-valued logic and assumes that the basic notion in logic is the proposition. First, we explain the distinction between the parts and the moments of a whole, and theories of ‘sortal terms’, two theories that will feature prominently. Second, we propose that logic comprises four ‘momental sectors’: the propositional and the functional calculi, the calculus of asserted propositions, and rules for (in)valid deduction, inference or substitution. Third, we elaborate on two neglected features of logic: the various modes of negating some part(s) of a proposition R, not only its ‘external’ negation not-R; and the assertion of R in the pair of propositions ‘it is (un)true that R’ belonging to the neglected logic of asserted propositions, which is usually left unstated. We also address the overlooked task of testing the asserted truth-value of R. Fourth, we locate logic among other foundational studies: set theory and other theories of collections, metamathematics, axiomatisation, definitions, model theory, and abstract and operator algebras. Fifth, we test this characterisation in two important contexts: the formulation of some logical paradoxes, especially the propositional ones; and indirect proof-methods, especially that by contradiction. The outcomes differ for asserted propositions from those for unasserted ones. Finally, we reflect upon self-referring self-reference, and on the relationships between logical and mathematical knowledge. A subject index is appended.

Formalization of Generalized Constraint Language: A Crucial Prelude to Computing With Words

The generalized constraint language (GCL), introduced by Zadeh, serves as a basis for computing with words (CW). It provides an agenda to express the imprecise and fuzzy information embedded in natural language and allows reasoning with perceptions. Despite its fundamental role, the definition of GCL has remained informal since its introduction by Zadeh, and to our knowledge, no attempt has been made to formulate a rigorous theoretical framework for GCL. Such formalization is necessary for further theoretical and practical advancement of CW for two important reasons. First, it provides the underlying infrastructure for the development of useful inference patterns based on sound theories. Second, it determines the scope of GCL and hence facilitates the translation of natural language expressions into GCL. This paper is an attempt to step in this direction by providing a formal syntax together with a compositional semantics for GCL. A soundness theorem is defined, and Zadeh's deduction rules are proved to be valid in the defined semantics. Furthermore, a discussion is provided on how the proposed language may be used in practice.

The Effect of Dynamic versus Static Assessment on Syntactic Development of Iranian College Preparatory EFL Learners

This study investigated the effect of dynamic assessment on learners’ syntactic knowledge. The main concern of this study was significant difference between dynamic and static assessment and the possible role of these two forms of assessment on the syntactic development of Iranian EFL college preparatory learners. To fulfill the purpose of the study, NELSON was administered to 70 pre university male learners. Those learners with scores one standard deviation above and below the mean were selected for the purpose of the study. There were 60 students who were then divided into experimental and control groups. Next, the pre-test (a teacher-made, multiple-choice test) was administered to 20 subjects of parallel group. Then, twelve multiple-choice grammar tests were administered to the subjects of the experimental group. The students received mediation in dynamic assessment model which involved some strategies like looking for clues, eliminating the answers that do not fit and comparison strategies. The mediation process was designed to enable teachers to mediate each of the items in an interactive way. The mediation was divided into two stages: a) manipulation of grammatical and structural point through the strategies mentioned above and b) information paper which was given to the students at the end of each session to work on them at home. The control group received deductive grammatical rules during twelve sessions. Finally, the pre-test was re-administered as the post-test and t-test was applied. The results showed that at 0.05 level of significance the mean of experimental group was more than the mean of control group for different scores and consequently the null-hypothesis was rejected. The study proved that dynamic assessment outperformed in improving syntactic knowledge of the learners.

A deductive system for proving workflow models from operational procedures

Many modern business environments employ software to automate the delivery of workflows; whereas, workflow design and generation remains a laborious technical task for domain specialists. Several different approaches have been proposed for deriving workflow models. Some approaches rely on process data mining approaches, whereas others have proposed derivations of workflow models from operational structures, domain specific knowledge or workflow model compositions from knowledge-bases. Many approaches draw on principles from automatic planning, but conceptual in context and lack mathematical justification. In this paper we present a mathematical framework for deducing tasks in workflow models from plans in mechanistic or strongly controlled work environments, with a focus around automatic plan generations. In addition, we prove an associative composition operator that permits crisp hierarchical task compositions for workflow models through a set of mathematical deduction rules. The result is a logical framework that can be used to prove tasks in workflow hierarchies from operational information about work processes and machine configurations in controlled or mechanistic work environments.

Granular Reasoning and Decision System’s Decomposition

In order to make further researches on decision logic, a generalized form of decision reasoning called granular reasoning is introduced, which is induced by the inclusion relation over granules, and is connected with granule’s operations. The investigations on it shows that granular reasoning not only covers a wider range including decision reasoning, but also satisfies the rules of deduction in classical logic. Thus, granular reasoning can be taken as a foundation to support decision reasoning. On the other hand, granular reasoning has close links with a decision system. Based on granular reasoning, a decision system can be divided into sub-decision systems. Consequently, as a special form of granular reasoning, decision reasoning defined in a decision system becomes to rely on sub-decision systems. This makes decision reasoning easier.

A Formalism for Action Representation Inspired by Mīmāṁsā

This paper endeavors to formalize imperatives that convey actions. Imperatives, unlike propositions, do not hold the value of true or false. Peter Vranas proposed an alternate logical formalism in the literature of imperative logic with three values, namely: Satisfaction (), Violation () and Avoidance (). Although this formalism takes into account the conditional imperatives, it does not address imperatives from the perspective of actions. According to Mīmāṁsā (one of the six systems of Indian philosophy), the prime motive of an imperative is to carry out action so as to reach the goal. This paper modifies the notion of Vranas' imperative logic using Mīmāṁsā principles. The resulting imperative formalism, focusing on action representation, is presented with syntax, deduction rules and semantic tables. The effectiveness of this representation is demonstrated in the area of artificial intelligence planning.

Structural Analysis of Boolean Equation Systems

We analyze the problem of solving Boolean equation systems through the use of structure graphs . The latter are obtained through an elegant set of Plotkin-style deduction rules. Our main contribution is that we show that equation systems with bisimilar structure graphs have the same solution. We show that our work conservatively extends earlier work, conducted by Keiren and Willemse, in which dependency graphs were used to analyze a subclass of Boolean equation systems, viz ., equation systems in standard recursive form . We illustrate our approach by a small example, demonstrating the effect of simplifying an equation system through minimization of its structure graph.

The Ins and Outs of Classifying Turnover for VAT

This article provides a brief insight into various topics. As a starting point, it describes which transactions form an economic activity for value-added tax (VAT) and are therefore within the scope of VAT. This is then put into the context of the economic reality of a business, whereby is assessed how turnover should be classified and what the effect is for VAT of such classification. In a nutshell, classification as usual turnover leads to deduction of VAT based on the general deduction rules. The classification as unusual turnover should not have any impact on the deduction of a company. Detailed guidance and the relevant ECJ case law on how to classify turnover are provided in this article. The final section of this article describes what the VAT treatment is of the sales of shares in the context of classification of turnover as well as the related consequences for the deduction.

Reasoning in Quantum Theory: Modus Ponens and the co-event interpretation

Classical logic does not apply in quantum theory. However one would like to be able to reason according to some standard rules for quantum systems as well (whether they are an electron or the universe itself). We examine what exactly is needed in order to be able to construct deductive arguments and in particular to maintain the "Modus Ponens" which is the basic deductive rule of inference. It turns out that this requirement restricts the possible theories and in the context of the coevent interpretation it results uniquely to the "multiplicative-scheme".

Superdeduction in Lambda-Bar-Mu-Mu-Tilde

Superdeduction is a method specially designed to ease the use of first-order theories in predicate logic. The theory is used to enrich the deduction system with new deduction rules in a systematic, correct and complete way. A proof-term language and a cut-elimination reduction already exist for superdeduction, both based on Christian Urban's work on classical sequent calculus. However the computational content of Christian Urban's calculus is not directly related to the (lambda-calculus based) Curry-Howard correspondence. In contrast the Lambda bar mu mu tilde calculus is a lambda-calculus for classical sequent calculus. This short paper is a first step towards a further exploration of the computational content of superdeduction proofs, for we extend the Lambda bar mu mu tilde calculus in order to obtain a proofterm langage together with a cut-elimination reduction for superdeduction. We also prove strong normalisation for this extension of the Lambda bar mu mu tilde calculus.

Abstracting and reasoning over ship trajectories and web data with the Simple Event Model (SEM)

Bridging the gap between low-level features and semantics is a problem commonly acknowledged in the Multimedia community. Event modeling can fill this gap by representing knowledge about the data at different level of abstraction. In this paper we present the Simple Event Model (SEM) and its application in a Maritime Safety and Security use case about Situational Awareness, where the data also come as low-level features (of ship trajectories). We show how we abstract over these low-level features, recognize simple behavior events using a Piecewise Linear Segmentation algorithm, and model the resulting events as instances of SEM. We aggregate web data from different sources, apply deduction rules, spatial proximity reasoning, and semantic web reasoning in SWI-Prolog to derive abstract events from the recognized simple events. The use case described in this paper comes from the Dutch Poseidon project.

Quantum coherent spaces and linear logic

Quantum Coherent Spaces were introduced by Girard as a quantum framework where to interpret the exponential-free fragment of Linear Logic. Aim of this paper is to extend Girard's interpretation to a subsystem of linear logic with bounded exponentials. We provide deduction rules for the bounded exponentials and, correspondingly, we introduce the novel notion of bounded exponentials of Quantum Coherent Spaces. We show that the latter provide a categorical model of our system. In order to do that, we first study properties of the category of Quantum Coherent Spaces.