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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]

Herman Geuvers
1994 Lecture Notes in Computer Science  
It is also possible to give 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.  ... 
doi:10.1007/3-540-58085-9_73 fatcat:sxlbfwdy4fbzfn63qoz4lcul6a

What Was the Syntax-Semantics Debate in the Philosophy of Science About?

Sebastian Lutz
2015 Philosophy and Phenomenological Research  
dependence 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.  ... 
doi:10.1111/phpr.12221 fatcat:aasjrgy3dvheln3mstpremkxge

Certified assembly programming with embedded code pointers

Zhaozhong Ni, Zhong Shao
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.  ... 
doi:10.1145/1111037.1111066 dblp:conf/popl/NiS06 fatcat:7xo5dvkvcjgafejdsa4bolpn6i

Formalizing Cut Elimination of Coalgebraic Logics in Coq [chapter]

Hendrik Tews
2013 Lecture Notes in Computer Science  
In their work on coalgebraic 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.  ... 
doi:10.1007/978-3-642-40537-2_22 fatcat:physiyzxlzbdhp76d2ptoil4xi

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

Christoph Wernhard
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.  ... 
doi:10.1007/978-3-642-41524-1_17 fatcat:zzzgdm5icjf65jtutn7eqwlqsa

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]

G. Bealer
1989 Studies in Linguistics and Philosophy  
P is 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))).  ... 
doi:10.1007/978-94-009-2721-6_7 fatcat:zbi272oufjg2pdy6fopj2p456e

The consistency of syntactical treatments of knowledge (How to compile quantificational modal logics into classical FOL)

Jim des Rivières, Hector J. Levesque
1988 Computational intelligence  
The relative expressive power 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.  ... 
doi:10.1111/j.1467-8640.1988.tb00088.x fatcat:jq35aqiiqrbuln6licx7bct7re

Processing for relevance

Marjolein Groefsema
1998 Revista Alicantina de Estudios Ingleses  
principie 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.  ... 
doi:10.14198/raei.1998.11.09 fatcat:i4spmrn5wjatjnkoq4zrfbrz74

THE CONSISTENCY OF SYNTACTICAL TREATMENTS OF KNOWLEDGE [chapter]

Jim des Rivières, Hector J. Levesque
1986 Theoretical Aspects of Reasoning About Knowledge  
The relative expressive power 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.  ... 
doi:10.1016/b978-0-934613-04-0.50011-9 fatcat:3bzwxno7kbgknjdlwzbrepa2le

On Spatial Conjunction as Second-Order Logic [article]

Viktor Kuncak, Martin Rinard
2004 arXiv   pre-print
On the side 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.  ... 
arXiv:cs/0410073v1 fatcat:ezlx6bafgzb5veyhymdgqr2rne

Sub-Sentential Logical Form. On Robert J. Stainton's Words and Thoughts

Axel Arturo Barceló Aspeitia
2011 Crítica. Revista Hispanoamericana de Filosofía  
Stainton argues (2006, 2001) that since sub-sentential speech acts lack the proper 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.  ... 
doi:10.22201/iifs.18704905e.2011.788 fatcat:au5sk4aurvapnfxy45umygjhhe

What's Right with a Syntactic Approach to Theories and Models?

Sebastian Lutz
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.  ... 
doi:10.1007/s10670-013-9578-5 fatcat:k27xvznxk5dj7kwuiat3mgbjti

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

Christoph Wernhard
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.  ... 
arXiv:1108.4891v1 fatcat:467vn5q6r5eftithdsuhzw7hdy
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