scholarly journals Predicate Change

2020 ◽  
Vol 49 (6) ◽  
pp. 1159-1183
Author(s):  
Corina Strößner
Keyword(s):  
Conceptual Change ◽  
Belief Revision ◽  
Predicate Logic ◽  
Expressive Power

AbstractLike belief revision, conceptual change has rational aspects. The paper discusses this for predicate change. We determine the meaning of predicates by a set of imaginable instances, i.e., conceptually consistent entities that fall under the predicate. Predicate change is then an alteration of which possible entities are instances of a concept. The recent exclusion of Pluto from the category of planets is an example of such a predicate change. In order to discuss predicate change, we define a monadic predicate logic with three different kinds of lawful belief: analytic laws, which hold for all possible instances; doxastic laws, which hold for the most plausible instances; and typicality laws, which hold for typical instances. We introduce predicate changing operations that alter the analytic laws of the language and show that the expressive power is not affected by the predicate change. One can translate the new laws into old laws and vice versa. Moreover, we discuss rational restrictions of predicate change. These limit its possible influence on doxastic and typicality laws. Based on the results, we argue that predicate change can be quite conservative and sometimes even hardly recognisable.

scholarly journals Conceptual Learning and Local Incommensurability: A Dynamic Logic Approach

Axiomathes ◽  
2021 ◽  
Author(s):  
Corina Strößner
Keyword(s):  
Conceptual Change ◽  
Belief Revision ◽  
Dynamic Logic ◽  
Expressive Power ◽  
Conceptual Learning ◽  
Rational Belief ◽  
Logical Analysis ◽  
Logical Reconstruction ◽  
Logical Study ◽  
Logic Approach

AbstractIn recent decades, the logical study of rational belief dynamics has played an increasingly important role in philosophy. However, the dynamics of concepts such as conceptual learning received comparatively little attention within this debate. This is problematic insofar as the occurrence of conceptual change (especially in the sciences) has been an influential argument against a merely logical analysis of beliefs. Especially Kuhn’s ideas about the incommensurability, i.e., untranslatability, of succeeding theories seem to stand in the way of logical reconstruction. This paper investigates conceptual change as model-changing operations similar to belief revision and relates it to the notion of incommensurability. I consider several versions of conceptual change and discuss their influences on the expressive power, translatability and the potential arising of incommensurability. The paper concludes with a discussion of animal taxonomy in Aristotle’s and Linnaeus’s work.

Embedding first order predicate logic in fragments of intuitionistic logic

1976 ◽  
Vol 41 (4) ◽  
pp. 705-718 ◽  
Author(s):  
M. H. Löb
Keyword(s):  
Intuitionistic Logic ◽  
Predicate Logic ◽  
Propositional Calculus ◽  
Expressive Power ◽  
Predicate Calculus ◽  
First Order ◽  
Intuitionistic Propositional Calculus ◽  
Individual Variables ◽  
The One ◽  
Order Predicate Calculus

Some syntactically simple fragments of intuitionistic logic possess considerable expressive power compared with their classical counterparts.In particular, we consider in this paper intuitionistic second order propositional logic (ISPL) a formalisation of which may be obtained by adding to the intuitionistic propositional calculus quantifiers binding propositional variables together with the usual quantifier rules and the axiom scheme (Ex), where is a formula not containing x.The main purpose of this paper is to show that the classical first order predicate calculus with identity can be (isomorphically) embedded in ISPL.It turns out an immediate consequence of this that the classical first order predicate calculus with identity can also be embedded in the fragment (PLA) of the intuitionistic first order predicate calculus whose only logical symbols are → and (.) (universal quantifier) and the only nonlogical symbol (apart from individual variables and parentheses) a single monadic predicate letter.Another consequence is that the classical first order predicate calculus can be embedded in the theory of Heyting algebras.The undecidability of the formal systems under consideration evidently follows immediately from the present results.We shall indicate how the methods employed may be extended to show also that the intuitionistic first order predicate calculus with identity can be embedded in both ISPL and PLA.For the purpose of the present paper it will be convenient to use the following formalisation (S) of ISPL based on [3], rather than the one given above.

scholarly journals COORDINATE-FREE LOGIC

2016 ◽  
Vol 9 (3) ◽  
pp. 522-555
Author(s):  
JOOP LEO
Keyword(s):  
Set Theory ◽  
Predicate Logic ◽  
Expressive Power ◽  
Free Logic ◽  
New Approach

AbstractA new logic is presented without predicates—except equality. Yet its expressive power is the same as that of predicate logic, and relations can faithfully be represented in it. In this logic we also develop an alternative for set theory. There is a need for such a new approach, since we do not live in a world of sets and predicates, but rather in a world of things with relations between them.

Is Language a Game?

1996 ◽  
Vol 26 (1) ◽  
pp. 1-28 ◽  
Author(s):  
Joseph Heath
Keyword(s):  
Game Theory ◽  
Social Life ◽  
Predicate Logic ◽  
Expressive Language ◽  
Expressive Power ◽  
Formal Models ◽  
Basic Action ◽  
Basic Assumptions ◽  
Recent Developments ◽  
Power Game

Recent developments in game theory have shown that the mathematical models of action so widely admired in the study of economics are in fact only particular instantiations of a more general theoretical framework. In the same way that Aristotelian logic was ‘translated’ into the more general and expressive language of predicate logic, the basic action theoretic underpinnings of modern economics have now been articulated within the more comprehensive language of game theory. But precisely because of its greater generality and expressive power, game theory has again revived the temptation to apply formal models of action to every domain of social life. This movement has been fuelled by some notable successes. Game theory has provided useful insights into the logic of collective action in the theory of public goods, and strategic models of voting have illustrated important aspects of institutional decision-making. But this extension of formal models into every area of social interaction has also encountered significant difficulties, despite the fact that contemporary decision theory has weakened its basic assumptions to the point where it teeters constantly on the brink of vacuity.

Noncompactness in propositional modal logic

1972 ◽  
Vol 37 (4) ◽  
pp. 716-720 ◽  
Author(s):  
S. K. Thomason
Keyword(s):  
Modal Logic ◽  
Predicate Logic ◽  
Expressive Power ◽  
Second Order ◽  
Order Logic ◽  
Relational Models ◽  
Propositional Modal Logic ◽  
Bimodal Logic ◽  
Deductive Power ◽  
Second Order Logic

We have come to believe that propositional modal logic (with the usual relational semantics) must be understood as a rather strong fragment of classical second-order predicate logic. (The interpretation of propositional modal logic in second-order predicate logic is well known; see e.g. [2, §1].) “Strong” refers of course to the expressive power of the languages, not to the deductive power of formal systems. By “rather strong” we mean sufficiently strong that theorems about first-order logic which fail for second-order logic usually fail even for propositional modal logic. Some evidence for this belief is contained in [2] and [3]. In the former is exhibited a finitely axiomatized consistent tense logic having no relational models, and the latter presents a finitely axiomatized modal logic between T and S4, such that □p → □2p is valid in all relational models of the logic but is not a thesis of the logic. The result of [2] is strong evidence that bimodal logic is essentially second-order, but that of [3] does not eliminate the possibility that unimodal logic only appears to be incomplete because we have not adopted sufficiently powerful rules of inference. In the present paper we present stronger evidence of the essentially second-order nature of unimodal logic.

scholarly journals Taking Up Thagard’s Challenge: A Formal Model of Conceptual Revision

2022 ◽  
Author(s):  
Sena Bozdag ◽  
Matteo De Benedetto
Keyword(s):  
Conceptual Change ◽  
Belief Revision ◽  
Formal Model ◽  
Conceptual Level ◽  
Conceptual Systems ◽  
Traditional Belief ◽  
Conceptual Structures

AbstractThagard (1992) presented a framework for conceptual change in science based on conceptual systems. Thagard challenged belief revision theorists, claiming that traditional belief-revision systems are able to model only the two most conservative types of changes in his framework, but not the more radical ones. The main aim of this work is to take up Thagard’s challenge, presenting a belief-revision-like system able to mirror radical types of conceptual change. We will do that with a conceptual revision system, i.e. a belief-revision-like system that takes conceptual structures as units of revisions. We will show how our conceptual revision and contraction operations satisfy analogous of the AGM postulates at the conceptual level and are able to mimic Thagard’s radical types of conceptual change.

scholarly journals Term Logic

Axioms ◽  
2020 ◽  
Vol 9 (1) ◽  
pp. 18 ◽  
Author(s):  
Peter Simons
Keyword(s):  
Propositional Logic ◽  
Predicate Logic ◽  
Expressive Power ◽  
Predominant Form ◽  
Term Logic ◽  
Empty Term ◽  
Inference Tree

The predominant form of logic before Frege, the logic of terms has been largely neglected since. Terms may be singular, empty or plural in their denotation. This article, presupposing propositional logic, provides an axiomatization based on an identity predicate, a predicate of non-existence, a constant empty term, and term conjunction and negation. The idea of basing term logic on existence or non-existence, outlined by Brentano, is here carried through in modern guise. It is shown how categorical syllogistic reduces to just two forms of inference. Tree and diagram methods of testing validity are described. An obvious translation into monadic predicate logic shows the system is decidable, and additional expressive power brought by adding quantifiers enables numerical predicates to be defined. The system’s advantages for pedagogy are indicated.

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