1.

A Proof Search System for a Modal Substructural Logic Based on Labelled Deductive Systems
- Hiu Fai Chau
This paper describes a proof search system for a non--classical logic (modal concatenation (substructural) logic) based on Gabbay's Labelled Deductive System (LDS). The logic concerned is treated as a case study. It has some unusual features which combine resource (linear, Lambek Calculus or relevance logics) with modality (intensional, temporal, or epistemic logics), and may have some useful applications in AI and natural language processing. We present axiomatic and LDS style proof theories (two-dimensional label structure) and semantics for the logic. Soundness and completeness results are proved. We show that, for non--classical logic theorem proving, LDS is more flexible than the...

2.

A Safe Relational Calculus for Functional Logic Deductive Databases?
Abstract. In this paper, we present an extended relational calculus for expressing queries in functional-logic deductive databases. This calculus is based on first-order logic and handles relation predicates, equalities and inequalities over partially defined terms, and approximation equations. For the calculus formulas, we have studied syntactic conditions in order to ensure the domain independence property. Finally, we have studied its equivalence w.r.t. the original query language which is based on equality and inequality constraints. 1

3.

Uncertainty and partial non-uniform assumptions in parametric deductive databases
- Yann Loyer; Umberto Straccia
Abstract. Different many-valued logic programming frameworks have been proposed to manage uncertain information in deductive databases and logic programming. A feature of these frameworks is that they rely on a predefined assumption or hypothesis, i.e. an interpretation that assigns the same default truth value to all the atoms of a program, e.g. in the open world assumption, by default all atoms have unknown truth value. In this paper we extend these frameworks along three directions: (i) we will introduce non-monotonic modes of negation; (ii) the default truth values of atoms need not necessarily to be all equal each other; and...

4.

Proofs, tests and continuation passing style
- Stefano Guerrini; Andrea Masini
The concept of syntactical duality is central in logic. In particular, the duality defined by classical negation, or more syntactically by left and right in sequents, has been widely used to relate logic and computations. We study the proof/test duality proposed by Girard in his 1999 paper on the meaning of logical rules. In details, starting from the notion of “test ” proposed by Girard, we develop a notion of test for intuitionistic logic and we give a complete deductive system whose computational interpretation is the target language of the call-by-value and call-by-name continuation passing style translations.

5.

Difference to Inference 1 Running Head: DIFFERENCE TO INFERENCE Difference to Inference: Teaching logical and statistical reasoning through online interactivity.
- Thomas E. Malloy
Difference to Inference is an online JAVA program simulating theory testing and falsification through research design and data collection in a game format. The program, based on cognitive and epistemological principles, is designed to support the learning of thinking skills underlying deductive and inductive logic and statistical reasoning. Difference to Inference has database connectivity so that game scores can be counted as part of course grades. Difference to Inference 3 Difference to Inference: Teaching logical and statistical reasoning through online interactivity Emphasizing the active nature of information processing, Posner and Osgood (1980) proposed that computers be used to train inquiry...

6.

Percepción de nuestros estudiantes acerca de las matemáticas en la vida diaria
- Mulero González, Julio; Segura Abad, Lorena; Sepulcre Martínez, Juan Matías
Las matemáticas constituyen un lenguaje universal, más concretamente son fundamentales para la ciencia y la ingeniería. Más aún, podríamos decir que son no sólo la base de todo conocimiento, sino también de cualquier tipo de desarrollo científico y tecnológico. Especialmente significante resulta que la física, la astronomía o la química dependen en buena medida de ellas y que son muy útiles en las ciencias económicas y sociales o en la informática. De hecho, ciencias como la filosofía o la psicología se valen de modelos matemáticos para la resolución de sus problemas. Las matemáticas forman una ciencia lógica y deductiva, y...

7.

A Modal Perspective on Proof Dynamics
- Patrick Allo
Core aim of this paper is to focus on the dynamics of real proofs by introducing the block-semantics from Batens (1995) as a dynamical counterpart for classical semantics. This approach reveals an informa-tional dynamics unknown to most dynamical logical systems. Viz. it adds an internal dynamics- due to deduction- to the better known external dynamics which is due to new information. A block-based weakening of modal epistemic logic avoiding logical (deductive) omniscience, is defined. It is subsequently extended with dynamic modal operators in order to gradually recapture the initial strength of modal epistemic logic. 1 Introduction and

8.

Difference to Inference 1 Running Head: DIFFERENCE TO INFERENCE Difference to Inference: Teaching logical and statistical reasoning through online interactivity.
- Thomas E. Malloy
Difference to Inference is an online JAVA program simulating theory testing and falsification through research design and data collection in a game format. The program, based on cognitive and epistemological principles, is designed to support the learning of thinking skills underlying deductive and inductive logic and statistical reasoning. Difference to Inference has database connectivity so that game scores can be counted as part of course grades. Difference to Inference 3 Difference to Inference: Teaching logical and statistical reasoning through online interactivity Emphasizing the active nature of information processing, Posner and Osgood (1980) proposed that computers be used to train inquiry...

9.

The State of Change: A Survey
- Anthony J. Bonner; Michael Kifer
. Updates are a crucial component of any database programming language. Even the simplest database transactions, such as withdrawal from a bank account, require updates. Unfortunately, updates are not accounted for by the classical Horn semantics of logic programs and deductive databases, which limits their usefulness in real-world applications. As a short-term practical solution, logic programming languages have resorted to handling updates using ad hoc operators without a logical semantics. A great many works have been dedicated to developing logical theories in which the state of the underlying database can evolve with time. Many of these theories were developed with...

10.

On Semantics, Syntactics and Fixpoints of General Programs
- Li Yan; Li Yan Yuan
In this paper, we extend the unified view of logic programs, characterized by van Emden and Kowalski, in terms of semantics, syntactics, and fixpoints into the context of general programs. We first propose a general model semantics which is a natural extension of the Herbrand model semantics. We have shown that any program has a unique least model. Then we show that the least model of a program is precisely the set of all minimally derived disjunctive facts from the program and reveal the relationship between semantics and syntactics of general programs. Finally we show that the least model of...

11.

Deriving Incremental Production Rules for Deductive Data
- Stefano Ceri; Jennifer Widom
We show that the production rule mechanism provided by active database systems can be used to quickly and easily implement the logic rule interface of deductive database systems. Deductive rules specify derived relations using Datalog with built-in predicates and stratified negation; the deductive rules are compiled automatically into production rules. We present a materialized approach, in which the derived relations are stored in the database and the production rules automatically and incrementally propagate base relation changes to the derived relations. We also present a non-materialized approach, in which the production rules compute the derived relations on demand. 1 Introduction A...

12.

Analysis of Sequential SLG Evaluation
- Terrance Swift; David S. Warren
SLG is a table-oriented resolution method that has the ability to combine the deductive database and logic programming paradigms. As an example of its applicability to deductive databases, SLG terminates and has polynomial data complexity for programs with finite models. In terms of the logic programming (and non-monotonic) paradigms, SLG computes the well-founded model for nonstratified programs, and has been extended to compute 3-valued stable model semantics. This paper presents performance analysis and comparisons of the SLG-WAM, an abstract machine for executing SLG. Firstly, the results indicate that the overhead of the SLG-WAM compared to a similar WAM implementation is...

13.

Explaining Program Execution in Deductive Systems
- Tarun Arora; Raghu Ramakrishnan; William G. Roth; Praveen Seshadri; Divesh Srivastava
this paper, we describe Explain, a menu-driven graphical tool for visualizing fact derivations in a logic programming/deductive database language. It is designed to operate in conjunction with the CORAL deductive database system [RSSS93b], and deals specifically with (extended) Horn-clause rules evaluated using bottom-up techniques. It differs significantly from debugging tools available for Prolog-style languages, which are designed for a top-down, backtracking evaluation strategy. A major difference between bottom-up and top-down strategies (used in Prolog-like systems) is that no guarantees are offered with respect to execution order in bottom-up evaluation, and thus, some non-operational abstraction of the computation must be used...

14.

Static Semantics For Normal and Disjunctive Logic Programs
- Teodor C. Przymusinski; Jack Minker
In this paper, we propose a new semantic framework for disjunctive logic programming by introducing static expansions of disjunctive programs. The class of static expansions extends both the classes of stable, well-founded and stationary models of normal programs and the class of minimal models of positive disjunctive programs. Any static expansion of a program P provides the corresponding semantics for P consisting of the set of all sentences logically implied by the expansion. We show that among all static expansions of a disjunctive program P there is always the least static expansion which we call the static completion P of...

15.

OOLP: A Translation Approach to Object-Oriented Logic Programming Deductive and Object-Oriented Databases
- Mukesh Dalal; Dipayan Gangopadhyay
OOLP integrates the superior modeling capabilities of object-oriented paradigm in the declarative framework of logic programming. Method invocation in OOLP is given a precise model theoretic semantics which is consistent with that of logic programming. OOLP is extended to a practical object-oriented database language OOLP+ by adding some extra-logical features. OOLP+ allows object identity, multiple inheritance, method overriding and dynamic updating among other features. OOLP+ is implemented by translating it to Prolog. The translated programs executes without metainterpretation. This allows the use of all Prolog or Datalog optimization techniques. In this respect OOLP+ is unique among alternative proposals presented in...

16.

Stable Semantics for Disjunctive Programs
- Teodor C. Przymusinski
We introduce the stable model semantics for disjunctive logic programs and deductive databases, which generalizes the stable model semantics, defined earlier for normal (i.e., non-disjunctive) programs. Depending on whether only total (2-valued) or all partial (3-valued) models are used we obtain the disjunctive stable semantics or the partial disjunctive stable semantics, respectively. The proposed semantics are shown to have the following properties: ffl For normal programs, the disjunctive (respectively, partial disjunctive) stable semantics coincides with the stable (respectively, partial stable) semantics. ffl For normal programs, the partial disjunctive stable semantics also coincides with the well-founded semantics. ffl For locally stratified...

17.

Adding Deductive Logic to a COTS Spreadsheet
- Marcelo Tallis; Teknowledge Corp; Rand Waltzman; Robert Balzer
We exploit the spreadsheet metaphor to make deductive problem-solving methods available to the vast population of spreadsheet end users. In particular, we show how the function-based problem-solving capabilities of spreadsheets can be extended to include logical deductive methods in a way that is consistent with the existing spreadsheet “look and feel. ” The foundation of our approach is the integration of a standard deductive logic system into a successful Commercial-Off-The-Shelf (COTS) spreadsheet. We have demonstrated this by designing and implementing an extension to Excel that manages the integration of Excel and a deductive logic engine based on the World Wide...

18.

Análisis comparativo de los programas oficiales de dibujo técnico en la enseñanza media y su implicación en las tecnologías de la información y de la comunicación (TIC) como recurso metodológico.
- GUIRAO SÁNCHEZ, ANA
Con la continua reducción horaria que han sufrido las enseñanzas artísticas a lo largo de las diferentes leyes de educación, y el tratamiento que sufren en cada una de ellas, estas enseñanzas quedan situadas como materia de necesidad variable.
Esto nos lleva ante un problema en bachillerato, cuyos alumnos que deciden cursar la asignatura de Dibujo Técnico, se ven perjudicados por la reducción de horas en la asignatura de Educación Plástica y Visual, ya que muchos de ellos llegan al bachillerato sin conocer conceptos básicos para el desarrollo de la asignatura de Dibujo Técnico.
Esta investigación quiere proponer una solución para compensar...

19.

Uncertainties in Knowledge Assessment
- Sylvia Encheva; Sharil Tumin
Abstract:- Various techniques for reasoning in the presence of inconsistent or incomplete information have been exploited lately. In this paper we focus on applying many-valued logic in practical deductive processes evaluating propositions being neither true nor false when they are uttered. Such situations occur while dealing with inconsistent and/or incomplete information. Application of many-valued logics allows the system to handle situations with such input. Many-valued logic is a generalization of Boolean logic and as such offers solution to a number of Boolean problems. Key-Words:- Web-based assessment, learning, intelligent tutoring systems 1

20.

Extending the Well-Founded and Valid Semantics for Aggregation
- S. Sudarshan; Divesh Srivastava; Raghu Ramakrishnan; Catriel Beeri
We present a very general technique for defining semantics for programs that use aggregation. We use the technique to extend the well-founded semantics and the valid semantics, both of which were designed to provide semantics for programs with negation, to handle programs that contain possibly recursive use of aggregation. The generalization is based on a simple but powerful idea of aggregation on three-valued multisets. The use of three-valued multisets makes our extended well-founded semantics, which we call aggregate-wellfounded semantics, easier to understand and more intuitive, in our opinion, than the extension of well-founded models by Van Gelder [14]. 1 Introduction...