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The Ricean Objection: An Analogue of Rice's Theorem for First-order Theories

I. C. Oliveira, W. Carnielli
2008 Logic Journal of the IGPL  
We propose here an extension of Rice's Theorem to first-order logic, proven by totally elementary means.  ...  If P is any property defined over the collection of all first-order theories and P is non-trivial over the set of finitely axiomatizable theories (i.e., P holds for some, but not all theories), then P  ...  Yoshikawa for useful discussions on the subject.  ... 
doi:10.1093/jigpal/jzn023 fatcat:g5rtchvccjc7zdaaeesekxncy4

Computational Hardness of Validity in Probability Logic [chapter]

Rutger Kuyper
2013 Lecture Notes in Computer Science  
We consider the complexity of validity in ε-logic, a probability logic introduced by Terwijn.  ...  We prove that the set of valid formulas is Π 1 1 -hard, improving a previous undecidability result by Terwijn.  ...  Previously, Terwijn [5] has shown that the set of ε-tautologies is undecidable. This should not be too surprising, because this is of course also the case for classical first-order logic.  ... 
doi:10.1007/978-3-642-35722-0_18 fatcat:afjzsro7nzdg7mljhcbjnzyawq

Page 5158 of Mathematical Reviews Vol. , Issue 2004g [page]

2004 Mathematical Reviews  
First, Tarski’s relation algebras (RAs) and representable relation algebras (RRAs) are introduced, and some classic undecidability results are mentioned.  ...  This theorem yields undecidability results for numerous sub- classes of relation algebras.  ... 

Page 2195 of Mathematical Reviews Vol. , Issue 2001D [page]

2001 Mathematical Reviews  
the undecidability of some sub-classical first-order logics.  ...  Summary: “A general criterion for the undecidability of sub- classical first-order logics and important fragments thereof is es- tablished.  ... 

A Survey on Temporal Logics [article]

Savas Konur
2011 arXiv   pre-print
This paper surveys main and recent studies on temporal logics in a broad sense by presenting various logic systems, dealing with various time structures, and discussing important features, such as decidability  ...  (or undecidability) results, expressiveness and proof systems.  ...  This makes temporal logics a richer notation than classical logics. Temporal logics can be considered as extensions of classical propositional and first-order logic.  ... 
arXiv:1005.3199v3 fatcat:nogsv2iggvd5likbkrnmnzpsdu

The Scope of Gödel's First Incompleteness Theorem

Bernd Buldt
2014 Logica Universalis  
for the job, as first-order logic is, then the axioms must be insufficient.  ...  Now replace 'Σ |= ϕ,' the relation of consequence (or informal reasoning if you will), with a set of logic rules R and formalized proofs based on it: Σ R ϕ.  ...  that it is possible to somehow control the explosion that occurs when one mixes classical logic with contradictions. 91 LP is a first-order logic whose semantics is based on Kleene's strong three-valued  ... 
doi:10.1007/s11787-014-0107-3 fatcat:n7ddz2nx3ndvngqvujtwvpeqgq

The Last Paper on the Halpern-Shoham Interval Temporal Logic [article]

Jerzy Marcinkowski, Jakub Michaliszyn
2010 arXiv   pre-print
The Halpern-Shoham logic is a modal logic of time intervals.  ...  Some effort has been put in last ten years to classify fragments of this beautiful logic with respect to decidability of its satisfiability problem.  ...  The satisfiability problem for the formulae of the logic of sub-intervals, over all discrete models, is undecidable. Preliminaries Orderings.  ... 
arXiv:1010.4529v1 fatcat:tdr7vzuqbbhjbnhwkjdp3f3tba

Page 1018 of Mathematical Reviews Vol. 34, Issue 5 [page]

1967 Mathematical Reviews  
To take care of this case the author indicates how to modify several axioms of first-order logic. (A possible interpretation of the new system was indicated by A.  ...  A formulation of the first-order predicate calculus is con- sidered in which only closed formulas (sentences) are al- lowed. It is well known (cf. footnote 6 and the remarks on page 7 of A.  ... 

Conflict without contradiction: paraconsistency and axiomatizable conflict toleration hierarchies in Evidence Logic

Don Faust
2004 Logic and Logical Philosophy  
Previous work has characterized the Boolean Sentence Algebras (BSAs) of the monadic, functional, and undecidable varieties of EL [4], [5] .  ...  Focusing on notions related to the degree of evidential conflict a theory may permit, we construct three hierarchies of axiomatizable extensions of EL and characterize the BSAs of the theories they entail  ...  As Popper [11, p. 59] said, Theories are nets to catch what we call 'the world': to rationalize, to explain, and to master it. We endeavor to make the mesh ever finer and finer.  ... 
doi:10.12775/llp.2001.009 fatcat:5ywe5wyw55evpi4j3x2p2eqvyi

Decidable and undecidable logics with a binary modality

�gnes Kurucz, Istv�n N�meti, Ildik� Sain, Andr�s Simon
1995 Journal of Logic, Language and Information  
We put an emphasis on the demonstration of proof-techniques, and hope that this will also help in finding the borderlines between decidable and undecidable fragments of usual first-order logic.  ...  Since associativity of"o" corresponds to commutativity of first-order existential quantifiers in some sense (cf. op cit), our results and techniques can help to find decidable fragments of first-order  ...  One of the key points was a "sub-method" for avoiding the assumption that our algebras have a discriminator term (which on the logic side amounts to expressibility of a universal modality), and still be  ... 
doi:10.1007/bf01049412 fatcat:ggzx4o3opbhqni6wbnhhpceeaa

Incompleteness, constructivism and truth

Fabrice Pataut
2014 Logic and Logical Philosophy  
Although Gödel proved the first incompleteness theorem by intuitionistically respectable means, Gödel's formula, true although undecidable, seems to offer a counter-example to the general constructivist  ...  recognized as such given the consistency and ω-consistency of P .  ...  I have benefited from criticisms and comments by Wilfrid Hodges and Jan Woleński when I gave a shortened version of the paper at the Second German-Polish Workshop on Logic and Logical Philosophy in Żagań  ... 
doi:10.12775/llp.1998.004 fatcat:c4d2cltrlfg6ff3briw4epspmq

Page 1021 of Mathematical Reviews Vol. 48, Issue 4 [page]

1974 Mathematical Reviews  
For a first order structure & and unary predicate p, let p(x) be the set of all elements of |./| (the universe of 7) 5847  ...  From this he obtains a number of coincidence results, e.g., for the theories SOA (successor and order arithmetic) and OR (order on the rationals).  ... 

Informal Provability, First-Order BAT Logic and First Steps Towards a Formal Theory of Informal Provability

Pawel Pawlowski, Rafal Urbaniak
2021 Logic and Logical Philosophy  
We also elaborate on the semantical properties of the first-order system and consider a couple of its strengthenings. It turns out that obtaining a sensible strengthening is not straightforward.  ...  BAT is a logic built to capture the inferential behavior of informal provability. Ultimately, the logic is meant to be used in an arithmetical setting.  ...  The work is supported by Polish National Science Centre (NCN) grant SONATINA 2 number 2018/28/C/HS1/00251 (Pawel Pawlowski) and grant SONATA BIS number 2016/22/E/HS1/ 00304 (Rafal Urbaniak).  ... 
doi:10.12775/llp.2021.016 fatcat:3dv435l3xfcklkknvxuleyly6u

Consistency and Decidability in Some Paraconsistent Arithmetics

Andrew Tedder
2021 The Australasian Journal of Logic  
The standard style of argument used to prove that a theory is unde- cidable relies on certain consistency assumptions, usually that some fragment or other is negation consistent.  ...  In a non-paraconsistent set- ting, this amounts to an assumption that the theory is non-trivial, but these diverge when theories are couched in paraconsistent logics.  ...  Applied Logic at Kansas State University and the Applied Mathematical Logic seminar at the Institute of Computer Science of the Czech Academy of Sciences, for discussion of early versions.  ... 
doi:10.26686/ajl.v18i5.6921 fatcat:ylxgkhrmava2po7kybx53izclq

Hybrid Metric Propositional Neighborhood Logics with Interval Length Binders

Dario Della Monica, Valentin Goranko, Guido Sciavicco
2011 Electronical Notes in Theoretical Computer Science  
In particular, we consider the natural hybrid extension of MPNL obtained by adding binders on integer variables ranging over lengths of intervals, thus enabling storage of the length of the current interval  ...  We investigate the question of how much hybrid machinery can be added to the interval neighbourhood logic PNL and its metric extension MPNL without losing the decidability of their satisfiability problem  ...  Both the interval logic ITL and DC are undecidable over almost all interesting classes of linear orders.  ... 
doi:10.1016/j.entcs.2011.06.009 fatcat:imdcxtvcrjfr5dusv52faaekfq
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