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Logical Consequence, Proof Theory, and Model Theory [chapter]

Stewart Shapiro
2005 The Oxford Handbook of Philosophy of Mathematics and Logic  
Set theory deals with the realm of models for model theory, and computability relates to the notion of a formal deductive system, in proof theory.  ...  Model theory and proof theory each provide for a notion of logical consequence, but the notions employed by these two branches are quite different from each other, at least conceptually.  ...  One might say that a form is logical if the only terms it contains (besides the schematic letters) are logical terms. We now face the task of characterizing the logical terms.  ... 
doi:10.1093/0195148770.003.0021 fatcat:t7mioins25cmpbyix4g3ehyhfm

Inferential Semantics [chapter]

Kosta Došen
2014 Dag Prawitz on Proofs and Meaning  
The frame for these opinions, and for the ensuing examination of those of Prawitz, is provided by what has been qualified as a dogmatic position that prooftheoretic semantics shares with model-theoretic  ...  Prawitz's views concerning inferences and their validity are examined in the light of opinions about general proof theory and proof-theoretic semantics inspired by categorial proof theory.  ...  In the classical, model-theoretical, case the correctness, i.e. validity, of a consequence relation, which is something hypothetical, is defined in terms of the preservation of the correctness, i.e. truth  ... 
doi:10.1007/978-3-319-11041-7_6 fatcat:gity7jghevbfhmj26e3ozbiwd4

Carnap's Early Metatheory: Scope and Limits [article]

Georg Schiemer, Richard Zach, Erich Reck
2015 arXiv   pre-print
In his Untersuchungen zur allgemeinen Axiomatik (1928) and Abriss der Logistik (1929), Rudolf Carnap attempted to formulate the metatheory of axiomatic theories within a single, fully interpreted type-theoretic  ...  framework and to investigate a number of meta-logical notions in it, such as those of model, consequence, consistency, completeness, and decidability.  ...  Richard Zach's research was supported by the Social Sciences and Humanities Research Council of Canada. We are grateful to A. W.  ... 
arXiv:1508.05867v1 fatcat:retw3jokk5hnxeffnw2hxw3gae

Carnap's early metatheory: scope and limits

Georg Schiemer, Richard Zach, Erich Reck
2015 Synthese  
In his Untersuchungen zur allgemeinen Axiomatik (1928) and Abriss der Logistik (1929), Rudolf Carnap attempted to formulate the metatheory of axiomatic theories within a single, fully interpreted type-theoretic  ...  framework and to investigate a number of meta-logical notions in it, such as those of model, consequence, consistency, completeness, and decidability.  ...  Richard Zach's research was supported by the Social Sciences and Humanities Research Council of Canada. We are grateful to A. W.  ... 
doi:10.1007/s11229-015-0877-z fatcat:okflkzou6ne7tmfj3eazqsj27u

Empirical Adequacy and Ramsification

J. Ketland
2004 British Journal for the Philosophy of Science  
One proposal is that the 'structural content' of a scientific theory may be associated with its Ramsey sentence ℜ(Θ).  ...  The structural realist who accepts a scientific theory Θ thinks that Θ is empirically correct, and furthermore is a realist about the 'structural content' of Θ.  ...  Axiomatic theories of truth over PA which do expand the Induction Scheme are sometimes non-conservative extensions (for example, the theory of truth based on the Tarskian inductive clauses).  ... 
doi:10.1093/bjps/55.2.287 fatcat:q7j5ogxehvgjtklpmsj64l3tku

Logic in the 1930s: Type Theory and Model Theory

Georg Schiemer, Erich H. Reck
2013 Bulletin of Symbolic Logic  
made in the type-theoretic tradition should be seen as central to the evolution of model theory.  ...  Indeed, the shift from type theory to first-order logic is sometimes seen as involving a radical break that first made possible the rise of modern model theory.  ...  To be more specific again, Tarski's notion of "correctness in all [sets] a" in Tarski [1935] is not identical with the modern notion of logical truth as specified in our Definition 3.  ... 
doi:10.1017/s1079898600010568 fatcat:muyww53stvedznv66scgumlrhi

Digitalization - relationship with the research area and education. One of the principal strategic directions of growth of agricultural land users

Valery P. DYACHKOV, Vyatka State Agricultural Academy, Russia, Elena V. SOFINA, Vyatka State Agricultural Academy, Russia
2021 Espacios  
The article reveals a new structure for the implementation of the electronic textbook for the study of the discipline "Financial Management" in the form of a system of electronic educational complexes  ...  This system includes twelve independent electronic educational complexes, each of which consists of five modules necessary for studying new material, developing practical skills in applying theoretical  ...  "Glossary" contains the list of the main notions and terms with corresponding definitions.  ... 
doi:10.48082/espacios-a21v42n01p02 fatcat:qym5eo5mafchnivesjm6wlmyou

Ramsey Sentence Realism as an Answer to the Pessimistic Meta‐Induction

Mark Newman
2005 Philosophy of Science  
We need some notion of what makes a theory legitimate such that its theoretical terms can then be used in subsequent theories as nontheoretical.  ...  As such, we end up with a translation of the original theory into entirely nontheoretical terms.  ... 
doi:10.1086/508975 fatcat:2yj3wpuxpjaurp56ckzp6ip37y

Incompleteness and the Romance of Science

Marvin Eli Kirsh
2008 Social Science Research Network  
It is argued that qualities of complete/incomplete science theory do not relate to the fertility or diversity or validity of science theory, but correspond with social, behavioral, moral values, and trespass  ...  into the realms of innate knowing, absolutes, cognition and behavior.  ...  As the environmental component consider the earth as a member of the set of terrains-having a location, and a complete theory, auto, that is self contained (as described).  ... 
doi:10.2139/ssrn.1281173 fatcat:hxkq67oogrhijkdqqhwlcftfce

Page 3124 of Mathematical Reviews Vol. , Issue 85g [page]

1985 Mathematical Reviews  
The notions of correctness are used in their strong sense, i.e., when started from good data, a partially correct program must not yield bad results; and a totally correct program must terminate properly  ...  {For the entire collection containing the first paper see MR 84f:68003b. } Stefan Sokolowski (Gdansk) Olderog, Ernst-Riidiger 85¢:68047 On the notion of expressiveness and the rule of adaptation.  ... 

Type-Theoretical Dynamics [chapter]

Giuseppe Primiero
2011 The Realism-Antirealism Debate in the Age of Alternative Logics  
In the light of the epistemic approaches to logic as agent-based procedures of knowledge, a basic dynamics for type theory is introduced.  ...  terms of default assumptions for such a structure; it adapts the usual revision operations and the analogous of the Ramsey test.  ...  Type Theory as a Theory of Beliefs The type-theoretical approach to belief revision provides a quite developed framework to treat with beliefs, expectations and justifications 5 .  ... 
doi:10.1007/978-94-007-1923-1_11 dblp:series/leus/Primiero12 fatcat:coslbvwdtjckvcjmtz3i76qqtq

Is Deflationism Compatible With Compositional and Tarskian Truth Theories? [chapter]

Lavinia Picollo, Thomas Schindler
2021 Modes of Truth  
Acknowledgments A first draft of this chapter was written while Thomas Schindler received support from the European Commission within the project The Logical Function of Property Talk (LOFUPRO, grant agreement  ...  In addition, both authors acknowledge the support of the German Research Council (DFG, Deutsche Forschungsgemeinschaft) within the project Reference Patterns of Paradox (GZ: PI 1294/1-1). Notes  ...  Thus, a natural theory of disquotation that implies them (given additional non-truth theoretic principles) would be the theory containing all instances of the T-schema.  ... 
doi:10.4324/9780429030208-3 fatcat:62d3pncqvzhabbdtap2sriq3jq

Logic in the 1930s: type theory and model theory

Georg Schiemer, Erich H. Reck
2013 Bulletin of Symbolic Logic  
For instance, let L 2 be a second-order extension of L in the sense that, in addition to the vocabulary of L, L 2 contains a denumerable number of relation variables (of every arity n).  ...  On that basis, the notion of satisfaction of a formula ϕ in a model M relative to an assignment s, in symbols M |= ϕ[s], can be defined by recursion on the complexity of formulas, as follows: 1.  ...  To be more specific again, Tarski's notion of "correctness in all [sets] a" in Tarski [1935] is not identical with the modern notion of logical truth as specified in our Definition 3.  ... 
doi:10.2178/bsl.1904010 fatcat:avxcxshqubco7f7qez2gsidexa

A Farewell to Falsifiability [article]

Douglas Scott, Ali Frolop, Ali Narimani, Andrei Frolov
2015 arXiv   pre-print
Some of the most obviously correct physical theories - namely string theory and the multiverse - make no testable predictions, leading many to question whether we should accept something as scientific  ...  We believe that we should also dispense with other outdated ideas, such as Fidelity, Frugality, Factuality and other "F" words. And we quote a lot of famous people to support this view.  ...  Fundamentals String theory and its close cousin, the notion of a multiverse, can solve all of the existing problems in theoretical physics [2] .  ... 
arXiv:1504.00108v1 fatcat:2evnydwfkfc65a7jg42ypyml4q

Page 5829 of Mathematical Reviews Vol. , Issue 93j [page]

1993 Mathematical Reviews  
The first part contains basic notions of error-correcting codes: parameters of codes, linear codes, decoding, Hamming and the binary Golay codes.  ...  An explicit description of the Hamming distance, as well as of any code distance, is also given, all in lattice-theoretic terms.  ... 
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