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We establish new, and surprisingly tight, connections between propositional proof complexity and finite model theory. ... By exploring these connections further, we establish finite-model-theoretic tools for proving lower bounds for the polynomial calculus over the rationals and over finite fields. ... bounds on the complexity of proofs (size and/or width/degree) for families of propositional formulas using arguments from finite model theory. ...arXiv:1802.09377v2 fatcat:uliyrq6kgjh3fnskxcuq6kq7py
Our novel, uniform approach to these lower bounds, Vol. 15:1 A FINITE-MODEL-THEORETIC VIEW ON PROPOSITIONAL PROOF COMPLEXITY 4:5 also suggests a way to capture a common weakness of many propositional proof ... VIEW ON PROPOSITIONAL PROOF COMPLEXITY 4:3 4:4 E. ... VIEW ON PROPOSITIONAL PROOF COMPLEXITY 4:21 Vol. 15:1 A FINITE-MODEL-THEORETIC VIEW ON PROPOSITIONAL PROOF COMPLEXITY 4:41 Vol. 15:1 A FINITE-MODEL-THEORETIC VIEW ON PROPOSITIONAL PROOF COMPLEXITY ...doi:10.18154/rwth-2019-00950 fatcat:3pbaatf56vctfmvsbhhwo4ncae
translation of any FO formula (that fails in all finite models), has degree proof complexity over fields of characteristic p, that behave in 4 distinct ways: (i) The degree complexity is bound by a constant ... (ii) The degree complexity is at least l(n) for all values of n. (iii) The degree complexity is bound by a constant on an infinite set S, and is at least l(n) on the complement N \ S. ... Another interesting question is if it possible to extend Krajicek's model theoretic approach to include model theoretical criteria that correspond to the fluctuating NS-degree (PC-degree) refutation complexity ...doi:10.1109/lics.2008.30 dblp:conf/lics/Riis08 fatcat:hij6dbovtvgirjnlph24ztbifu
The aim of this note is to prove that for any wif D of E there is a finite set of wffs having properties similar to some properties of a finite model.” 02D _ Proof theory See also 10293, 10332, 10334, ... - sions of formalized w-consistency; formalized completeness no- tions; unique and explicitly definable fixed points on propositions; conservation results based on formalized consistency; model-theo- retic ...
Our main tools are (a) model theoretic techniques and (b) a systematic study of the pure derived category of an additive finitely accessible category. ... Given a locally coherent Grothendieck category G, we prove that the homotopy category of complexes of injective objects (also known as the coderived category of G) is compactly generated triangulated. ... Since each perfect complex has finitely presentable cohomology by the above proposition, we can view D perf (fp G) as a thick subcategory of D b (fp G). ...arXiv:1412.1615v1 fatcat:ieemca6vqncsnioxiuvgdqwkoi
“In this paper, we introduce the notion of a model-theoretic property and formulate general principles of defining lists of prop- erties that are important in constructions of finitely axiomatizable theories ... On the basis of these results, existence theorems and estimates for the algorithmic complexity of natural semantic classes of sentences were also obtained. ...
Special topics include a chapter on transducers (finite state automata with output strings) and a section on random access machines (modelling the classical von Neumann-style computer), the latter shown ... the isomorphism front (25-41); Paul Beame and Toniann Pitassi, Propositional proof complexity: past, present, and future (42-70); Neil Immer- man, Progress in descriptive complexity (71-82); Jack H. ...
We investigate extensions of tenlporal logic by finite automata on infinite words. ... There are three different types of acceptance conditions (finite, looping and repeating) that one can give for these finite automata. This gives rise to three different logics. ... automata-theoretic point of view. ...doi:10.1109/sfcs.1983.51 dblp:conf/focs/WolperVS83 fatcat:5j7n26m36vbyfcri4zfpc3qque
The areas of recursion theory, proof theory and logic for computer science, model theory, and set theory are discussed independently. ... I am grateful to Yiannis Moschovakis, Richard Shore, John Steel, and Hugh Woodin for their comments on an earlier draft of this section. ... More broadly, much work in weak first-order theories and on propositional proof complexity is motivated by the desire to find a logical proof that P = NP. Future problems in proof complexity. ...arXiv:cs/0205003v1 fatcat:i3rpwamx6nfdzi5kqkrt34twkq
In finite model theory, it is the complexity of describing properties, whereas in proof complexity it is the complexity of proving properties in a proof system. ... In particular, we show how the complexity of logics in the setting of finite model theory is used to obtain results in bounded arithmetic, stating which functions are provably total in certain weak systems ... The results on connections between finite model theory and bounded arithmetic mentioned here come from my joint work with Stephen Cook (which resulted in my PhD thesis). ...doi:10.1093/logcom/exq008 fatcat:lpla27ghunf5fmmvdanaoasaei
The author views this system as a use- ful bridge between the tree proof rules for propositional logic and those for first-order logic. ... Summary: “We define minimal consequence in sentential logic and present a number of results of a model-theoretic and recursion- theoretic character about this newly introduced nonmonotonic con- sequence ...
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This note aims to examine critically Kripke's semantics for propositional intuitionistic logic. ... Kripke's semantic is extensionally correct with respect to propositional intuitionistic logic, that is, the calculus is sound and complete with respect to the semantics. ... Proof: straightforward induction on the complexity of A. ...doaj:1e58cf2d10594ad599a45c0a9b49d64a fatcat:kg4y6ev2jffdfkc4dyibhtnxle
The areas of recursion theory, proof theory and logic for computer science, model theory, and set theory are discussed independently. ... I am grateful to Yiannis Moschovakis, Richard Shore, John Steel, and Hugh Woodin for their comments on an earlier draft of this section. ... More broadly, much work in weak first-order theories and on propositional proof complexity is motivated by the desire to find a logical proof that P j-NP. Future problems in proof complexity. ...doi:10.2307/2687773 fatcat:mdamfnfy55atzalpnh7ul3xv6m
It contains a description of the standard format of adaptive logics, analyses the notion of dynamic proof required by those logics, discusses the means to turn such proofs into demonstrations, and argues ... that, notwithstanding their formal complexity, adaptive logics are important because they explicate an abundance of reasoning forms that occur frequently, both in scientific contexts and in common sense ... A proof-theoretic procedure was devised, first for propositional CL by Batens and Provijn (2001) , and next for propositional CLuN r by Batens (2005) . ...doi:10.1007/s11229-007-9268-4 fatcat:if5ehjgolba7pat3vw3gp25nze
(2) What is the complexity of deciding whether M is an undominated model of a pair (I',A), where I is a propositional formula in conjunctive normal form and A is a set of 2-literal defaults? ... H. 03 MATHEMATICAL LOGIC AND FOUNDATIONS 6170 Papadimitriou: (1) What is the complexity of finding a minimal model of a propositional formula when all the letters are mini- mized? ...
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