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Coalgebraic Infinite Traces and Kleisli Simulations [article]

Natsuki Urabe, Ichiro Hasuo
2018 arXiv   pre-print
There, following Jacobs' work, infinitary trace semantics is characterized as the "largest homomorphism."  ...  Kleisli simulation is a categorical notion introduced by Hasuo to verify finite trace inclusion. They allow us to give definitions of forward and backward simulation for various types of systems.  ...  infinitary tree languages of such systems.  ... 
arXiv:1505.06819v3 fatcat:a4ioxfm5izf5bk5rrfupiskpaq

Preservation theorems for strong first-order logics [article]

Christian Espíndola
2019 arXiv   pre-print
Another consequence of our approach is the equivalence of the Vopěnka principle and a general definability theorem on subsets preserved by homomorphisms.  ...  Lyndon) on sentences of L_ω_1, ω preserved by substructures (resp. homomorphic images).  ...  axioms: R(x) ∧ R * (x) ⊢ x ⊥ ⊤ ⊢ x R(x) ∨ R * (x) The homomorphisms in the new language will then correspond to embeddings and by hypothesis φ is preserved.  ... 
arXiv:1906.09173v2 fatcat:xsjvwnf4azhxfc3sl3iwh2rq5a

Some characterization theorems for infinitary universal Horn logic without equality

Pilar Dellunde, Ramon Jansana
1996 Journal of Symbolic Logic (JSL)  
In this paper we mainly study preservation theorems for two fragments of the infinitary languages L κ κ , with κ regular, without the equality symbol: the universal Horn fragment and the universal strict  ...  In spite of this, in the field of abstract algebraic logic we find a theorem which, properly translated, is a preservation result for the strict universal Horn fragment of infinitary languages without  ...  Czelakowski and J. Flum for some conversations (personal or by e-mail) on the content of the paper and also the last two for their comments and suggestions to improve a first version of it.  ... 
doi:10.2307/2275814 fatcat:v5rrlcl74rco7pvcqlmlsnqtuy

Page 4694 of Mathematical Reviews Vol. , Issue 93i [page]

1993 Mathematical Reviews  
Belegradek (Kemerovo) 93i:03045 03C40 03C75 Hyttinen, Tapani (SF-HELS) Preservation by homomorphisms and infinitary languages. Notre Dame J. Formal Logic 32 (1991), no.2, 167-172.  ...  The main re- sults of the paper are devoted to the question of when sentences of the languages are preserved by homomorphisms and have equiva- lent sentences which are in normal form.  ... 

An extension of Jónsson-Tarski representation and model existence in predicate non-normal modal logics [article]

Yoshihito Tanaka
2021 arXiv   pre-print
In this paper, we give an extension of the Jónsson-Tarski representation theorem for both normal and non-normal modal algebras so that it preserves countably many infinitary meets and joins.  ...  We also show the same results for infinitary modal logics.  ...  It is easy to see that f is a homomorphism of Boolean algebras. We show f preserves modal operator.  ... 
arXiv:2103.16857v1 fatcat:wppkuytghvfmnelszqlco63jnq

On the adequacy of graph rewriting for simulating term rewriting

J. R. Kennaway, J. W. Klop, M. R. Sleep, F. J. de Vries
1994 ACM Transactions on Programming Languages and Systems  
, preservation of normal forms, preservation of reduction, and cofinality.  ...  Infinitary graph rewriting may be formalized by analogy with infinitary term rewriting.  ...  Both U(G) and D(G) are closed under finite reduction by U(R) and the subterm relation. PROOF. We consider first U(G). Let t G U(G), and let t + t'by reduction of a redex r by a rule in U(R).  ... 
doi:10.1145/177492.177577 fatcat:7eyaob6drfh3tkukuinorwzauy

Axiomatizations of universal classes through infinitary logic

Michał M. Stronkowski
2018 Algebra Universalis  
We use infinitary sentences there. New proofs of Birkhoff's HSPtheorem and Mal'cev's SPP U -theorem are derived. In total, we present 75 facts of this sort.  ...  This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/ by/4.0/), which permits unrestricted use, distribution, and  ...  We would like to express our deep gratitude to Marcel Jackson and Tomasz Kowalski for the inspiration and kind hospitality. Open Access.  ... 
doi:10.1007/s00012-018-0507-y fatcat:7etb3v3cxrbdjalcnqgo75u464

Birkhoff Completeness in Institutions

Mihai Codescu, Daniel Găină
2008 Logica Universalis  
This result is then applied to the particular cases of Horn clauses logic, the 'Horn fragment' 1 of preorder algebras, order-sorted algebras and partial algebras and their infinitary variants. (2000) .  ...  We develop an abstract proof calculus for logics whose sentences are 'Horn sentences' of the form: (∀X)H =⇒ c and prove an institutional generalization of Birkhoff completeness theorem.  ...  Mihai Codescu has been supported by a PhD scholarship of DFKI Laboratory, Bremen. Daniel Gȃinȃ has been supported by a PhD scholarship of Japan Advanced Institute of Science and Technology.  ... 
doi:10.1007/s11787-008-0035-1 fatcat:fyouzdhrsnavfippnsc7jdvnfy

Convergence in Infinitary Term Graph Rewriting Systems is Simple (Extended Abstract)

Patrick Bahr
2013 Electronic Proceedings in Theoretical Computer Science  
In this extended abstract, we present a simple approach to convergence on term graphs that allows us to unify term graph rewriting and infinitary term rewriting.  ...  The only unfavourable property that we were able to identify, viz. failure of full correspondence between weak metric and partial order convergence, is rectified by adopting a strong convergence discipline  ...  Convergence in Infinitary Term Graph Rewriting Systems is Simple (Extended Abstract) Unfortunately, we do not have solid soundness or completeness results for weak convergence apart from the preservation  ... 
doi:10.4204/eptcs.110.4 fatcat:bar5l5ch6zh5dbfsdi4zzwdjae

Exact Unification and Admissibility

George Metcalfe, Leonardo Cabrer, Franz Baader
2015 Logical Methods in Computer Science  
A new hierarchy of "exact" unification types is introduced, motivated by the study of admissible rules for equational classes and non-classical logics.  ...  Minimal complete sets of unifiers under this new preordering always have a smaller or equal cardinality than those provided by the standard instantiation preordering, and in significant cases a dramatic  ...  Consider a language with one binary operation, written as juxtaposition, and two constants 0 and 1.  ... 
doi:10.2168/lmcs-11(3:23)2015 fatcat:surhjqyr3rgsxm5punoyisea2e

Duality for modal μ-logics

Chrysafis Hartonas
1998 Theoretical Computer Science  
We focus here on Kozen's [21] p-calculi, both finitary and infinitary.  ...  The modal p-calculi are extensions of propositional modal logics with least and greatest fixpoint operators.  ...  For the infinitary system, where the homomorphisms on the algebras are required to preserve the (possibly) infinitary joins involved in the definition of the unfoldings of the fixpoint terms, the characterization  ... 
doi:10.1016/s0304-3975(97)00233-8 fatcat:bkuwgqcg2fg6lmhw55wds2a5vm

Page 1630 of Mathematical Reviews Vol. 49, Issue 5 [page]

1975 Mathematical Reviews  
The basic tool is Lyndon’s preservation theorem: the first order formulas preserved under homomorphisms are exactly the positive formulas. G. Cherlin (Heidelberg) 8854 Keisler, H.  ...  The technique of indiscernibles, introduced into finitary logic by Ehrenfeucht and Mostowski, is developed for infinitary logic in Part II (Chapters 13-20).  ... 

Page 2104 of Mathematical Reviews Vol. 57, Issue 6 [page]

1979 Mathematical Reviews  
Let B be a countably complete Boolean algebra and 57 #16050 h: By | L->B a homomorphism preserving infinite bounds.  ...  Constantin Milici (Timisoara) Cunningham, Ellen Chain models: applications of consistency properties and back- | and-forth techniques in infinite-quantifier languages. j Infinitary logic: in memoriam Carol  ... 

Exact Unification [article]

Leonardo Cabrer, George Metcalfe
2014 arXiv   pre-print
A new hierarchy of "exact" unification types is introduced, motivated by the study of admissibility for equational classes and non-classical logics.  ...  Minimal complete sets of unifiers under this new preordering always have a smaller or equal cardinality than those provided by the standard instantiation preordering, and in significant cases a dramatic  ...  Let ( ) X : E V (Σ, Y ) → E V (Σ, X) be the map defind by σ → σ X . It is clear that ( ) X preserves ⊑ V and that σ X ↾ Y = σ for each σ ∈ E V (Σ, Y ).  ... 
arXiv:1410.5583v1 fatcat:pyyts7prgjbtpcydjtwygahwha

Positive model theory and infinitary logic [article]

Jean Berthet
2015 arXiv   pre-print
The topology is Hausdorff, has the Baire property, and its compactness characterises positive model completeness; it also has a basis of clopen sets and is described by the formulas of geometric logic.  ...  This shows how "positive ω-saturation" is a fundamental connection between positive and infinitary logic, and we suggest a geometric analogue of positive Morleyisation.  ...  By the fact, L-homomorphisms from A into a model of T are essentially the models of T u ∪ D + A in the language L(A).  ... 
arXiv:1403.2540v3 fatcat:5hl7tp6k2rfubefzcxd4h7htme
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