Toward Formalizing Usefulness in Propositional Language

2006 ◽  
pp. 650-661
Author(s):  
Yi Zhou ◽  
Xiaoping Chen
Keyword(s):  
Propositional Language

scholarly journals The heterogeneity of mental representation: Ending the imagery debate

2015 ◽  
Vol 112 (33) ◽  
pp. 10089-10092 ◽  
Author(s):  
Joel Pearson ◽  
Stephen M. Kosslyn
Keyword(s):  
20Th Century ◽  
Mental Representation ◽  
Historical Context ◽  
Internal Representations ◽  
The Past ◽  
Different Types ◽  
Imagery Debate ◽  
Propositional Language

The possible ways that information can be represented mentally have been discussed often over the past thousand years. However, this issue could not be addressed rigorously until late in the 20th century. Initial empirical findings spurred a debate about the heterogeneity of mental representation: Is all information stored in propositional, language-like, symbolic internal representations, or can humans use at least two different types of representations (and possibly many more)? Here, in historical context, we describe recent evidence that humans do not always rely on propositional internal representations but, instead, can also rely on at least one other format: depictive representation. We propose that the debate should now move on to characterizing all of the different forms of human mental representation.

Gentzen sequent calculi for some intuitionistic modal logics

2019 ◽  
Vol 27 (4) ◽  
pp. 596-623
Author(s):  
Zhe Lin ◽  
Minghui Ma
Keyword(s):  
Propositional Logic ◽  
Sequent Calculus ◽  
Modal Logics ◽  
Cut Elimination ◽  
Sequent Calculi ◽  
Intuitionistic Propositional Logic ◽  
Propositional Language ◽  
Intuitionistic Modal Logics ◽  
Subformula Property ◽  
Gentzen Sequent Calculus

Abstract Intuitionistic modal logics are extensions of intuitionistic propositional logic with modal axioms. We treat with two modal languages ${\mathscr{L}}_\Diamond $ and $\mathscr{L}_{\Diamond ,\Box }$ which extend the intuitionistic propositional language with $\Diamond $ and $\Diamond ,\Box $, respectively. Gentzen sequent calculi are established for several intuitionistic modal logics. In particular, we introduce a Gentzen sequent calculus for the well-known intuitionistic modal logic $\textsf{MIPC}$. These sequent calculi admit cut elimination and subformula property. They are decidable.

scholarly journals VOLUNTARY IMAGINATION: A FINE-GRAINED ANALYSIS

2020 ◽  
pp. 1-26
Author(s):  
ILARIA CANAVOTTO ◽  
FRANCESCO BERTO ◽  
ALESSANDRO GIORDANI
Keyword(s):  
Cognitive Psychology ◽  
Subject Matter ◽  
Philosophy Of Mind ◽  
Formal Semantics ◽  
Mental Simulation ◽  
Fine Grained ◽  
Logic Of Imagination ◽  
New Knowledge ◽  
Propositional Language ◽  
Core Features

Abstract We study imagination as reality-oriented mental simulation (ROMS): the activity of simulating nonactual scenarios in one’s mind, to investigate what would happen if they were realized. Three connected questions concerning ROMS are: What is the logic, if there is one, of such an activity? How can we gain new knowledge via it? What is voluntary in it and what is not? We address them by building a list of core features of imagination as ROMS, drawing on research in cognitive psychology and the philosophy of mind. We then provide a logic of imagination as ROMS which models such features, combining techniques from epistemic logic, action logic, and subject matter semantics. Our logic comprises a modal propositional language with non-monotonic imagination operators, a formal semantics, and an axiomatization.

On the structure of early language

2021 ◽  
Author(s):  
Tania Kuteva ◽  
Bernd Heine
Keyword(s):  
Social Exchange ◽  
Language Processing ◽  
Speech Act ◽  
Language Evolution ◽  
Hierarchical Organization ◽  
Comprehensive Understanding ◽  
Early Language ◽  
Modes Of Processing ◽  
Propositional Language ◽  
Complementary Analysis

Both linguistic and neuroanatomical evidence suggests that there are two modes of processing in linguistic discourse, namely an analytic mode and a holistic mode. Competent speakers of a language know many linguistic entities in two ways: holistically and analytically, and can move between the two. The analytic mode is concerned with propositional language processing based on the compositional format of sentences, clauses, and phrases and their hierarchical organization, while the holistic mode surfaces mainly in unanalyzable, formulaic expressions, for example, in speech act formulas such as interjections (wow, ouch), ideophones (bang, splish-splash), formulae of social exchange (hello, sorry, goodbye). Research on the reconstruction of earlier stages of language evolution has for the most part been restricted to the analytic mode, and grammaticalization theory played an important role in this research. The present chapter demonstrates that a complementary analysis of holistic ways of processing can contribute to a more comprehensive understanding of how human languages may have evolved.

The finite model property in tense logic

1995 ◽  
Vol 60 (3) ◽  
pp. 757-774 ◽  
Author(s):  
Frank Wolter
Keyword(s):  
Modal Logics ◽  
Tense Logic ◽  
Finite Model ◽  
Model Property ◽  
Finite Model Property ◽  
Negative Results ◽  
Propositional Language ◽  
Positive Results

AbstractTense logics in the bimodal propositional language are investigated with respect to the Finite Model Property. In order to prove positive results techniques from investigations of modal logics above K4 are extended to tense logic. General negative results show the limits of the transfer.

Completeness and decidability of tense logics closely related to logics above K4

1997 ◽  
Vol 62 (1) ◽  
pp. 131-158 ◽  
Author(s):  
Frank Wolter
Keyword(s):  
Modal Logics ◽  
Finite Width ◽  
Propositional Language

AbstractTense logics formulated in the bimodal propositional language are investigated with respect to Kripke-completeness (completeness) and decidability. It is proved that all minimal tense extensions of modal logics of finite width (in the sense of K. Kine) as well as all minimal tense extensions of cofinal subframe logics (in the sense of M. Zakharyaschev) are complete. The decidability of all finitely axiomatizable minimal tense extensions of cofinal subframe logics is shown. A number of variations and extensions of these results are also presented.

Idea selection for propositional language production

2020 ◽  
pp. 1-24
Author(s):  
Megan S. Barker ◽  
Amelia Ceslis ◽  
Gail A. Robinson
Keyword(s):  
Language Production ◽  
Propositional Language ◽  
Selection For

Modal semantics without possible worlds

1981 ◽  
Vol 46 (1) ◽  
pp. 77-86 ◽  
Author(s):  
John T. Kearns
Keyword(s):  
Possible Worlds ◽  
The Other ◽  
Modal Operator ◽  
Logical Operators ◽  
Semantic Account ◽  
Necessary Truth ◽  
Modal Semantics ◽  
Propositional Language ◽  
Image Position ◽  
Plain Truth

In this paper I will develop a semantic account for modal logic by considering only the values of sentences (and formulas). This account makes no use of possible worlds. To develop such an account, we must recognize four values. These are obtained by subdividing (plain) truth into necessary truth (T) and contingent truth (t); and by subdividing falsity into contingent falsity (f) and necessary falsity (impossibility: F). The semantic account results from reflecting on these concepts and on the meanings of the logical operators.To begin with, we shall consider the propositional language L0. The language L0 has (1) infinitely many atomic sentences, (2) the two truth-functional connectives ∼, ∨, and the modal operator □. (Square brackets are used for punctuation.) The other logical expressions are defined as follows:D1 [A & B] = (def)∼[∼A ∨ ∼ B],D2 [A ⊃ B] = (def)[∼A ∨ B],D3 ◊ A =(def)∼□∼A.I shall use matrices to give partial characterizations of the significance of logical expressions in L0. For negation, this matrix is wholly adequate:Upon reflection, it should be clear that this matrix is the obviously correct matrix for negation.

scholarly journals A Study of Anomia: Evidence for a Distinction Between Nominal and Propositional Language

Cortex ◽  
1994 ◽  
Vol 30 (2) ◽  
pp. 231-245 ◽  
Author(s):  
Kristin Breen ◽  
Elizabeth K. Warrington
Keyword(s):  
Propositional Language
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