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Page 5463 of Mathematical Reviews Vol. , Issue 2002H
[page]

2002
*
Mathematical Reviews
*

As

*a**syntactic*analogue*of*Tarski’s truth*predicate*, the authors introduce the notion*of**syntactical*truth*predicate*(s.t.p.) for the*second**order*arithmetic PA’, also denoted Z> elsewhere. ... Whereas Tarski’s*predicate*is*a*third*order*object, s.t.p. is just*a*set*of*closed formulas*of**second**order*arithmetic and so it remains*of**second**order*. ...##
###
Conservativity between logics and typed λ calculi
[chapter]

1994
*
Lecture Notes in Computer Science
*

It is also possible to give

doi:10.1007/3-540-58085-9_73
fatcat:sxlbfwdy4fbzfn63qoz4lcul6a
*a**syntactic*proof by defining*a*mapping from*propositions*and proofs*of**second**order**propositional**logic*to first*order**propositional**logic*that preserves derivability. ...*of*the formulas-as-types*embedding*are not complete, like the*embedding**of*higher*order**predicate**logic**into*the Calculus*of*Constructions. ...##
###
What Was the Syntax-Semantics Debate in the Philosophy of Science About?

2015
*
Philosophy and Phenomenological Research
*

dependence

doi:10.1111/phpr.12221
fatcat:aasjrgy3dvheln3mstpremkxge
*of**syntactic*and semantic approaches. ... The debate between critics*of**syntactic*and semantic approaches to the formalization*of*scientific theories has been going on for over 40 years. ... But they fail to work once you take*into*account that in model theory, structures already come with*a*language*of**predicate**logic*. So one has to take language*into*account. ...##
###
Certified assembly programming with embedded code pointers

2006
*
Conference record of the 33rd ACM SIGPLAN-SIGACT symposium on Principles of programming languages - POPL'06
*

*Embedded*code pointers (ECPs) are stored handles

*of*functions and continuations commonly seen in low-level binaries as well as functional or higher-

*order*programs. ... By adding

*a*small amount

*of*syntax to the assertion language, we show how to combine semantic consequence relation with

*syntactic*proof techniques. ... Acknowledgments We thank Hai Fang, Xinyu Feng, Nadeem

*A*. ...

##
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Formalizing Cut Elimination of Coalgebraic Logics in Coq
[chapter]

2013
*
Lecture Notes in Computer Science
*

In their work on coalgebraic

doi:10.1007/978-3-642-40537-2_22
fatcat:physiyzxlzbdhp76d2ptoil4xi
*logics*, Pattinson and Schröder prove soundness, completeness and cut elimination in*a*generic sequent calculus for*propositional*multi-modal*logics*[1]. ... The formalization exploits dependent types to obtain*a*very concise deep*embedding*for formulas and proofs. ... Prop is the type*of**propositions*, which may or may not have*a*proof. Similar to higher-*order**logic*,*a*set over*A*is conveniently modeled as*a*function*A*→ Prop. ...##
###
Computing with Logic as Operator Elimination: The ToyElim System
[chapter]

2013
*
Lecture Notes in Computer Science
*

*A*prototype system is described whose core functionality is, based on

*propositional*

*logic*, the elimination

*of*

*second*-

*order*operators, such as Boolean quantifiers and operators for projection, forgetting ... This approach allows to express many representational and computational tasks in knowledge representation -for example computation

*of*abductive explanations and models with respect to

*logic*programming ... Conclusion We have seen

*a*prototype system for computation with

*logic*as elimination

*of*

*second*-

*order*operators. ...

##
###
Page 2862 of Mathematical Reviews Vol. , Issue 87f
[page]

1987
*
Mathematical Reviews
*

Summary: “It has been proposed that some posets

*of*quantum*logic*could be*embedded**into*lattices in*order*to recover the lattice structure while avoiding the introduction*of*‘ad hoc’ axioms. We ... This paper is more than*a*very well-written survey*of*Friedman’s research on subsystems*of**second*-*order*arithmetic. ...##
###
Fine-Grained Type-Free Intensionality
[chapter]

1989
*
Studies in Linguistics and Philosophy
*

P is

doi:10.1007/978-94-009-2721-6_7
fatcat:zbi272oufjg2pdy6fopj2p456e
*a*prelinear*ordering*on D that induces*a*partition*of*D*into*subdomains H' E K ) . ... He begins with the premise that an arbitrary first-*order*necessitysentence 'N[*A*(F 1 , ••• , Fn)I' -where 'F 1 ', ••• , 'Fn ' are the*predicates*occurring in*A*-is true in*a*model if and only if the*second*-*order*...*A*prominent example is the 'Geach Rule': changetype (*a*,b) to ((c,*a*),(c,b)); which can be used, e.g., to lift sentence negation (type (t, t)) to*predicate*negation (type (( e, t), ( e, t))). ...##
###
The consistency of syntactical treatments of knowledge (How to compile quantificational modal logics into classical FOL)

1988
*
Computational intelligence
*

The relative expressive power

doi:10.1111/j.1467-8640.1988.tb00088.x
fatcat:jq35aqiiqrbuln6licx7bct7re
*of**a*sentential operator U]o~ is compared to that*of**a**syntactical**predicate*L('c~') in the setting*of*first-*order**logics*. ... Despite results by Montague and by Thomason that claim otherwise, any*of*the so-called CCmodal"*logics**of*knowledge and belief can be translated*into*classical first-*order**logics*that have*a*corresponding ... Definition ¢ is an eztended theorem ifffor every*embedding*o*of*~1 in ~(L), ¢o is*a*theorem*of*first-*order**logic*. ...##
###
Processing for relevance

1998
*
Revista Alicantina de Estudios Ingleses
*

principie

doi:10.14198/raei.1998.11.09
fatcat:i4spmrn5wjatjnkoq4zrfbrz74
*of*relevance, by building anticipatory hypotheses about the overall*propositional*form*of*the utterance. ... This paper addresses the question*of*what the consequences*of*this claim are for*a*model on on-line input processing, and proposes*a*model in which addressees interpret utterances in accordance with the ... concerning those concepts help or hinder completion*of*the*logical*hypotheses*into**a**propositional*form. ...##
###
THE CONSISTENCY OF SYNTACTICAL TREATMENTS OF KNOWLEDGE
[chapter]

1986
*
Theoretical Aspects of Reasoning About Knowledge
*

The relative expressive power

doi:10.1016/b978-0-934613-04-0.50011-9
fatcat:3bzwxno7kbgknjdlwzbrepa2le
*of**a*sentential operator U]o~ is compared to that*of**a**syntactical**predicate*L('c~') in the setting*of*first-*order**logics*. ... Despite results by Montague and by Thomason that claim otherwise, any*of*the so-called CCmodal"*logics**of*knowledge and belief can be translated*into*classical first-*order**logics*that have*a*corresponding ... Definition ¢ is an eztended theorem ifffor every*embedding*o*of*~1 in ~(L), ¢o is*a*theorem*of*first-*order**logic*. ...##
###
On Spatial Conjunction as Second-Order Logic
[article]

2004
*
arXiv
*
pre-print

On the side

arXiv:cs/0410073v1
fatcat:ezlx6bafgzb5veyhymdgqr2rne
*of*decidability, the*embedding**into**second*-*order**logic*immediately implies the decidability*of*first-*order**logic*with*a*form*of*spatial conjunction over trees. ... We construct an*embedding*from first-*order**logic*with spatial conjunction*into**second*-*order**logic*, and more surprisingly, an*embedding*from full*second**order**logic**into*first-*order**logic*with spatial conjunction ... The consequences*of*the translation from*second*-*order**logic*to spatial conjunction for two-variable*logic*with counting were crystallized in discussion with Greta Yorsh. ...##
###
Sub-Sentential Logical Form. On Robert J. Stainton's Words and Thoughts

2011
*
Crítica. Revista Hispanoamericana de Filosofía
*

Stainton argues (2006, 2001) that since sub-sentential speech acts lack the proper

doi:10.22201/iifs.18704905e.2011.788
fatcat:au5sk4aurvapnfxy45umygjhhe
*syntactic*structure to have*logical*form, it is not from them that subsententially*propositions*conveyed derive their ...*of*sub-sentential speech, they also satisfy all the criteria put forward by him to be the primary bearers*of**logical*form. ... The first one plays the role*of**predicate*, and the*second**of*subject. This is what it means to say that they are*logically*related in*predication*. ...##
###
What's Right with a Syntactic Approach to Theories and Models?

2014
*
Erkenntnis: An International Journal of Scientific Philosophy
*

*Syntactic*approaches in the philosophy

*of*science, which are based on formalizations in

*predicate*

*logic*, are often considered in principle inferior to semantic approaches, which are based on formalizations ... To compare the two kinds

*of*approach, I identify some ambiguities in common semantic accounts and explicate the concept

*of*

*a*structure in

*a*way that avoids hidden references to

*a*specific vocabulary. ... The use

*of*higher

*order*

*predicate*

*logic*

*Second*

*order*

*logic*is already enough "to capture directly most all mathematical practice" (Leivant 1994, 260; cf. ...

##
###
Computing with Logic as Operator Elimination: The ToyElim System
[article]

2011
*
arXiv
*
pre-print

*A*prototype system is described whose core functionality is, based on

*propositional*

*logic*, the elimination

*of*

*second*-

*order*operators, such as Boolean quantifiers and operators for projection, forgetting ... This approach allows to express many representational and computational tasks in knowledge representation - for example computation

*of*abductive explanations and models with respect to

*logic*programming ... Conclusion We have seen

*a*prototype system for computation with

*logic*as elimination

*of*

*second*-

*order*operators. ...

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