A computational algorithm for the verification of tautologies in propositional calculus

A computational algorithm (based on Smullyan's analytic tableau method) that varifies whether a given well-formed formula in propositional calculus is a tautology or not has been implemented on a DEC system 10. The stepwise refinement approch of program development used for this implementation forms the subject matter of this paper. The top-down design has resulted in a modular and reliable program package. This computational algoritlhm compares favourably with the algorithm based on the well-known resolution principle used in theorem provers.

An algorithm for inferring multivalued dependencies that works also for a subclass of propositional logic /

"UILU-ENG 79 1714."

Os paradoxos de Prior e o calculo proposicional deôntico relevante E¹.

Cruz, Ângela Maria Paiva. Os paradoxos de Prior e o cálculo proposicional deôntico relevante. Princípios, Natal, v. 4, p. 05-18, 1996.

Sobre quantificadores: uma formalização do quantificador 'quase sempre'

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

A neighbourhood semantic for the Logic TK

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Non-normal modal logics, quantification, and deontic dilemmas. A study in multi-relational semantics

This dissertation is devoted to the study of non-normal (modal) systems for deontic logics, both on the propositional level, and on the first order one. In particular we developed our study the Multi-relational setting that generalises standard Kripke Semantics. We present new completeness results concerning the semantic setting of several systems which are able to handle normative dilemmas and conflicts. Although primarily driven by issues related to the legal and moral field, these results are also relevant for the more theoretical field of Modal Logic itself, as we propose a syntactical, and semantic study of intermediate systems between the classical propositional calculus CPC and the minimal normal modal logic K.

Inference rules for unsatisfiability /

UIUCDCS-R-79-955

Mental logic and its difficulties with disjunction

The mental logic theory does not accept the disjunction introduction rule of standard propositional calculus as a natural schema of the human mind. In this way, the problem that I want to show in this paper is that, however, that theory does admit another much more complex schema in which the mentioned rule must be used as a previous step. So, I try to argue that this is a very important problem that the mental logic theory needs to solve, and claim that another rival theory, the mental models theory, does not have these difficulties.

Os paradoxos de Prior e o calculo proposicional deôntico relevante E¹.

Cruz, Ângela Maria Paiva. Os paradoxos de Prior e o cálculo proposicional deôntico relevante. Princípios, Natal, v. 4, p. 05-18, 1996.

Os paradoxos de Prior e o calculo proposicional deôntico relevante E¹.

Cruz, Ângela Maria Paiva. Os paradoxos de Prior e o cálculo proposicional deôntico relevante. Princípios, Natal, v. 4, p. 05-18, 1996.

An automata theoretic decision procedure for the propositional mu-calculus

The propositional mu-calculus is a propositional logic of programs which incorporates a least fixpoint operator and subsumes the propositional dynamic logic of Fischer and Ladner, the infinite looping construct of Streett, and the game logic of Parikh. We give an elementary time decision procedure, using a reduction to the emptiness problem for automata on infinite trees. A small model theorem is obtained as a corollary.

Modeling obligations with event-calculus

Time plays an important role in norms. In this paper we start from our previously proposed classification of obligations, and point out some shortcomings of Event Calculus (EC) to represent obligations. We proposed an extension of EC that avoids such shortcomings and we show how to use it to model the various types of obligations.

Insight into the fractional calculus via a spreadsheet

Many students of calculus are not aware that the calculus they have learned is a special case (integer order) of fractional calculus. Fractional calculus is the study of arbitrary order derivatives and integrals and their applications. The article begins by stating a naive question from a student in a paper by Larson (1974) and establishes, for polynomials and exponential functions, that they can be deformed into their derivative using the μ-th order fractional derivatives for 0<μ<1. Through the power of Excel we illustrate the continuous deformations dynamically through conditional formatting. Some applications are discussed and a connection made to mathematics education.

Permissions in Deontic Event-Calculus

Permissions are special case of deontic effects and play important role compliance. Essentially they are used to determine the obligations or prohibitions to contrary. A formal language e.g., temporal logic, event-calculus et., not able to represent permissions is doomed to be unable to represent most of the real-life legal norms. In this paper we address this issue and extend deontic-event-calculus (DEC) with new predicates for modelling permissions enabling it to elegantly capture the intuition of real-life cases of permissions.

Solution of a System of Generalized Abel Integral Equations Using Fractional Calculus

A method is presented for obtaining useful closed form solution of a system of generalized Abel integral equations by using the ideas of fractional integral operators and their applications. This system appears in solving certain mixed boundary value problems arising in the classical theory of elasticity.