Predicate Logic

2013 ◽  
pp. 109-129
Author(s):  
Faron Moller ◽  
Georg Struth
Keyword(s):  
Predicate Logic

AN INTENSIONAL LEIBNIZ SEMANTICS FOR ARISTOTELIAN LOGIC

2010 ◽  
Vol 3 (2) ◽  
pp. 262-272 ◽  
Author(s):  
KLAUS GLASHOFF
Keyword(s):  
Natural Deduction ◽  
Predicate Logic ◽  
Formal System ◽  
Aristotelian Logic ◽  
Categorical Logic ◽  
Characteristic Numbers ◽  
Formal Syntax ◽  
Philosophical Standpoint ◽  
Classical Philosophy

Since Frege’s predicate logical transcription of Aristotelian categorical logic, the standard semantics of Aristotelian logic considers terms as standing for sets of individuals. From a philosophical standpoint, this extensional model poses problems: There exist serious doubts that Aristotle’s terms were meant to refer always to sets, that is, entities composed of individuals. Classical philosophy up to Leibniz and Kant had a different view on this question—they looked at terms as standing for concepts (“Begriffe”). In 1972, Corcoran presented a formal system for Aristotelian logic containing a calculus of natural deduction, while, with respect to semantics, he still made use of an extensional interpretation. In this paper we deal with a simple intensional semantics for Corcoran’s syntax—intensional in the sense that no individuals are needed for the construction of a complete Tarski model of Aristotelian syntax. Instead, we view concepts as containing or excluding other, “higher” concepts—corresponding to the idea which Leibniz used in the construction of his characteristic numbers. Thus, this paper is an addendum to Corcoran’s work, furnishing his formal syntax with an adequate semantics which is free from presuppositions which have entered into modern interpretations of Aristotle’s theory via predicate logic.

Syllogism and quantification

1962 ◽  
Vol 27 (1) ◽  
pp. 58-72 ◽  
Author(s):  
Timothy Smiley
Keyword(s):  
Predicate Logic ◽  
Modern Logic ◽  
First Order ◽  
First Order Predicate Logic

Anyone who reads Aristotle, knowing something about modern logic and nothing about its history, must ask himself why the syllogistic cannot be translated as it stands into the logic of quantification. It is now more than twenty years since the invention of the requisite framework, the logic of many-sorted quantification.In the familiar first-order predicate logic generality is expressed by means of variables and quantifiers, and each interpretation of the system is based upon the choice of some class over which the variables may range, the only restriction placed on this ‘domain of individuals’ being that it should not be empty.

Some logical and syntactical observations concerning the first-order dependent type system λP

1999 ◽  
Vol 9 (4) ◽  
pp. 335-359 ◽  
Author(s):  
HERMAN GEUVERS ◽  
ERIK BARENDSEN
Keyword(s):  
Predicate Logic ◽  
Type System ◽  
Logical Framework ◽  
First Order ◽  
Logical Derivation ◽  
Dependent Type ◽  
First Order Predicate Logic

We look at two different ways of interpreting logic in the dependent type system λP. The first is by a direct formulas-as-types interpretation à la Howard where the logical derivation rules are mapped to derivation rules in the type system. The second is by viewing λP as a Logical Framework, following Harper et al. (1987) and Harper et al. (1993). The type system is then used as the meta-language in which various logics can be coded.We give a (brief) overview of known (syntactical) results about λP. Then we discuss two issues in some more detail. The first is the completeness of the formulas-as-types embedding of minimal first-order predicate logic into λP. This is a remarkably complicated issue, a first proof of which appeared in Geuvers (1993), following ideas in Barendsen and Geuvers (1989) and Swaen (1989). The second issue is the minimality of λP as a logical framework. We will show that some of the rules are actually superfluous (even though they contribute nicely to the generality of the presentation of λP).At the same time we will attempt to provide a gentle introduction to λP and its various aspects and we will try to use little inside knowledge.

First order predicate logic

1986 ◽  
pp. 155-183
Author(s):  
Igor Aleksander ◽  
Henri Farreny ◽  
Malik Ghallab
Keyword(s):  
Predicate Logic ◽  
First Order ◽  
First Order Predicate Logic

scholarly journals Higher-Order Illative Combinatory Logic

2013 ◽  
Vol 78 (3) ◽  
pp. 837-872 ◽  
Author(s):  
Łukasz Czajka
Keyword(s):  
Strong Consistency ◽  
Predicate Logic ◽  
Higher Order ◽  
Second Order ◽  
Model Construction ◽  
Partial Answer ◽  
Combinatory Logic ◽  
First Order ◽  
Propositional Quantifiers

AbstractWe show a model construction for a system of higher-order illative combinatory logic thus establishing its strong consistency. We also use a variant of this construction to provide a complete embedding of first-order intuitionistic predicate logic with second-order propositional quantifiers into the system of Barendregt, Bunder and Dekkers, which gives a partial answer to a question posed by these authors.

Modelling spatial reasoning systems with shape algebras and formal logic

1997 ◽  
Vol 11 (4) ◽  
pp. 273-285 ◽  
Author(s):  
Scott C. Chase
Keyword(s):  
Spatial Reasoning ◽  
Predicate Logic ◽  
Spatial Relations ◽  
Large Set ◽  
First Order ◽  
Reasoning Systems ◽  
Geometric Objects ◽  
Small Set ◽  
Definition Of ◽  
High Level

AbstractThe combination of the paradigms of shape algebras and predicate logic representations, used in a new method for describing designs, is presented. First-order predicate logic provides a natural, intuitive way of representing shapes and spatial relations in the development of complete computer systems for reasoning about designs. Shape algebraic formalisms have advantages over more traditional representations of geometric objects. Here we illustrate the definition of a large set of high-level design relations from a small set of simple structures and spatial relations, with examples from the domains of geographic information systems and architecture.

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