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Implication and analysis in classical frege structures

1987
*
Annals of Pure and Applied Logic
*

M (5)

doi:10.1016/0168-0072(87)90040-6
fatcat:iwkfjwsjcfehnmndhkyewotb6y
*Implication**and**analysis**in**classical**Frege**structures*37*and*M e {x I'"x } (6) are interdeducible. ... (11)*Implication**and**analysis**in**classical**Frege**structures*39 If now we define I = SKK we get Ix = SgKx = = x. So I is the identity function on everything. ... Let us now therefore develop the theory of (Dedekind) real numbers*and*a bit of elementary*analysis*using our hierarchy of*implications*. ...##
###
Page 35 of Mathematical Reviews Vol. , Issue 97A
[page]

1997
*
Mathematical Reviews
*

*In*this paper, we investigate

*classical*substructural logics consisting of

*implication*

*and*negation. How- ever, our method is general enough to apply to rich systems beyond the fragment. ... It is well known that

*in*simply typed lambda calculus, the notion of formulas-as-types makes it possible to find fine

*structure*of the

*implicational*fragment of intuitionistic logic, i.e., relevance logic ...

##
###
Page 3032 of Mathematical Reviews Vol. , Issue 89F
[page]

1989
*
Mathematical Reviews
*

89:0 3046
89f:03046 03E70 03B40 03F60
Flagg, Robert C. (1-OHS); Myhill, John (1-SUNYB)

*Implication**and**analysis**in**classical**Frege**structures*. Ann. Pure Appl. Logic 34 (1987), no. 1, 33-85. ...*In*this paper the authors develop the proof theory*and*model theory of*classical**Frege**structures*, formalize the hierarchy of*implications*, prove the consistency of the system*and*outline the resulting ...##
###
Deflationary Truth and the Problem of Relativistic Grounds of Emotivism

2019
*
VOLUME-8 ISSUE-10, AUGUST 2019, REGULAR ISSUE
*

The essence of the problem is explained, which consists

doi:10.35940/ijitee.a9222.119119
fatcat:yintntg5jna53busdd2smjlg2y
*in*the impossibility to make a logical conclusion*in*a situation of mixed contexts, when the antecedent has a value meaning,*and*the consequent is ... The paper describes how recognition of an emotive content by moral statements*in*the form of attitudes leads to the emergence of the*Frege*-Geach problem. ... The*Frege*-Geach problem arises when we consider the*implication**and*logical conclusion assuming the non-cognitive thesis that moral statements are not statements, but attitudes. ...##
###
Page 3539 of Mathematical Reviews Vol. , Issue 2004e
[page]

2004
*
Mathematical Reviews
*

Some approaches

*in*each conception are philosophical*and*some are mathematical*in*character, their common assumption being that they reflect a previous intuition—*in*some cases—already at work*in**classical*... Most of this paper is an intricate*and*delicate alge- braic*analysis*of various forms of inverse compositionality. ...##
###
Logic as Calculus and Logic as Language: Too Suggestive to be Truthful?

2021
*
Philosophia Scientiæ
*

Abstract: The paper focuses on the inferential role of quantifiers

doi:10.4000/philosophiascientiae.2816
fatcat:uun7ug3ckzfntdjwwvf3lao7ne
*in**Frege*, Peano*and*Russell. ... questions, as embodied*in*Jean van Heijenoort's well-known dictum about "logic as calculus*and*logic as language." ... C C Even*implication*elimination*and*some other rules with independent premisses, say A*and*B*in*the introduction of a conjunction A&B are thus displayed, which opens the possibility to analyse the*structure*...##
###
Author index volume 34 (1987)

1987
*
Annals of Pure and Applied Logic
*

degrees (1) EPSTEIN, R.L., see COOPER, S.B. (1) FLAGG, R.C.

doi:10.1016/0168-0072(87)90071-6
fatcat:sgh6etqckncjhhkjigjimlvemy
*and*FRIEDMAN, H., Maximality*in*modal logic (2) FLAGG, R.C.*and*MYHILL, J.,*Implication**and**analysis**in**classical**Frege**structures*(1) FRIEDMAN ... ., Categoricity*in*hyperarithmetical degrees (1) BALDWIN, J.T.*and*HARRINGTON, L., Trivial pursuit: Remarks on the main gap (3) COOPER, S.B.*and*EPSTEIN, R.L., Complementing below recursively enumerable ...##
###
Frege on Consistency and Conceptual Analysis

2007
*
Philosophia Mathematica
*

*Analysis*

*in*

*Frege*: a Brief Overview Conceptual

*analysis*is crucial to all of Frege's logicist

*and*proto-logicist work. ... sees it,

*Frege*

*and*Hilbert have no disagreement over the role of conceptual

*analysis*

*in*logical investigation,

*and*hence their disagreement over consistency-proofs cannot be explained

*in*the way just ...

*structure*of the pre-analytic sentences

*in*question. ...

##
###
Page 619 of Mathematical Reviews Vol. , Issue 92b
[page]

1992
*
Mathematical Reviews
*

The axioms for a

*Frege**structure*can be proved*in*this theory. ... the truth-table conditions*and*standard quantifier rules without the grammatical conditions*in*the corresponding axioms for a*Frege**structure*. ...##
###
Page 4221 of Mathematical Reviews Vol. , Issue 89H
[page]

1989
*
Mathematical Reviews
*

*Frege*would only have re- jected model-theoretic characterizations of logical notions, such as logical validity,

*implication*

*and*equivalence.) ... Such a subsystem, Friedman’s WKLh, is discussed by the author, along with a list of important theorems of

*classical*

*analysis*

*and*algebra that have been proved

*in*WKL» (mainly by the author

*and*/or D. ...

##
###
Proof Complexity of Non-classical Logics
[chapter]

2012
*
Lecture Notes in Computer Science
*

Due their richer expressivity

doi:10.1007/978-3-642-31485-8_1
fatcat:o2gh5kqzp5fpvb3fataonggkz4
*and*numerous applications within computer science, also non-*classical*logics have been intensively studied from a proof complexity perspective*in*the last decade,*and*a number ...*In*these notes we give an introduction to this recent field of proof complexity of non-*classical*logics. We cover results from proof complexity of modal, intuitionistic,*and*non-monotonic logics. ... Acknowledgements We are very grateful to Rosalie Iemhoff*and*Emil Jeřábek for numerous helpful comments on an earlier version of these notes. ...##
###
Page 5563 of Mathematical Reviews Vol. , Issue 90J
[page]

1990
*
Mathematical Reviews
*

It follows from this result that provability

*in*the pure*classical**implication*calculus is co-NP complete. E. ... The author proposes that some*structures*can be described*in*both “static” terms*and**in*“dynamic” terms using a set of ideal con- structions. ...##
###
FACETS OF INTENSIONALITY

2021
*
ARHE
*

We will argue that despite the common belief, intensional aspects of mathematical notions can be,

doi:10.19090/arhe.2020.34.61-83
fatcat:aao5d7jncna53pxipoblya5dfq
*and**in*fact have been successfully described*in*mathematics. ... Our considerations result*in*defending a) the importance of a rule-based semantical approach*and*b) the position according to which non-reductive*and*somewhat circular explanations play an essential role ... According to his account, the main difference between an intuitionist*and*a*classical*logician is that while*in**classical*logic the*implication*is understood truth-functionally, the intuitionistic*implication*...##
###
Rational hermeneutics and paraconsistency

2004
*
Logic and Logical Philosophy
*

*Frege*

*in*his paper from 1918 "The Thought: a Logical Inquiry" [

*Frege*1967 ],

*in*fact, set an example of such an

*analysis*when he envisages a vicious circle

*in*the definition of truth. ... Meanwhile, the recent investigations discovered the presence of paraconsistent

*structure*within the depth of

*classical*logics. As it was show by J.-Y. ...

##
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Understanding Gentzen and Frege Systems for QBF

2016
*
Proceedings of the 31st Annual ACM/IEEE Symposium on Logic in Computer Science - LICS '16
*

Here we provide a comprehensive

doi:10.1145/2933575.2933597
dblp:conf/lics/BeyersdorffP16
fatcat:drqb2sqeybhzfgbrlwbjaiosni
*analysis*of the new extended*Frege*system from [10], denoted EF + ∀red, which is a natural extension of*classical*extended*Frege*EF. ... Finally, we show that unconditional lower bounds for EF + ∀red would imply either a major breakthrough*in*circuit complexity or*in**classical*proof complexity,*and**in*fact the converse*implications*hold ... Acknowledgments This research was supported by grant no. 48138 from the John Templeton Foundation*and*EPSRC grant EP/L024233/1. ...
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