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Well-foundedness of term orderings [chapter]

M. C. F. Ferreira, H. Zantema
1995 Lecture Notes in Computer Science  
Well-foundedness is the essential property of orderings for proving termination.  ...  The usual path orders fulfil this criterion, yielding a much simpler proof of well-foundedness than the classical proof depending on Kruskal's theorem.  ...  But since non-well-foundedness of> would imply non-well-foundedness of ~ (by an argument similar to the proof of theorem 4.1.2), we are done.  ... 
doi:10.1007/3-540-60381-6_7 fatcat:4v44jhewljazrliphlu3uj2ak4

Extensions to the Estimation Calculus [chapter]

Jeremy Gow, Alan Bundy, Ian Green
1999 Lecture Notes in Computer Science  
Our calculus enables automatic proofs of the well-foundedness of a large class of induction rules not captured by the original calculus.  ...  Walther's estimation calculus was designed to prove the termination of functional programs, and can also be used to solve the similar problem of proving the well-foundedness of induction rules.  ...  can be used to induce a well-founded relation m , de ned by 8x y: : ; x m y $ m(x) m(y) The estimation calculus 10] attempts to prove sets of well-foundedness formulae using the well-founded size order  ... 
doi:10.1007/3-540-48242-3_16 fatcat:aw243rxzz5heln6zk2f23pzobq

A proof assistant for symbolic model-checking [chapter]

J. C. Bradfield
1993 Lecture Notes in Computer Science  
It also provides help with checking the well-foundedness conditions required to prove liveness properties.  ...  We describe a prototype of a tool to assist in the modelchecking of infinite systems by a tableau-based method.  ...  'X Window System' is a trademark of the Massachusetts Institute of Technology.  ... 
doi:10.1007/3-540-56496-9_25 fatcat:z33vuw456jcd3kpalg5e4ete2a

Verifying an Applicative ATP Using Multiset Relations [chapter]

Francisco J. Martín-Mateos, Jose A. Alonso, María J. Hidalgo, José L. Ruiz-Reina
2001 Lecture Notes in Computer Science  
We have carried out a mechanical proof of this property in the ACL2 logic. This allows us to provide well-founded multiset relations in order to prove termination of recursive functions.  ...  Every relation on a set A induces a relation on finite multisets over A; it can be shown that the multiset relation induced by a well-founded relation is also wellfounded [3] .  ...  Multisets provide a powerful way to prove termination in some of these non trivial cases. Multisets are usually defined in an informal way as "sets with repeated elements".  ... 
doi:10.1007/3-540-45654-6_47 fatcat:qkpblk2rxjhvlcgeckgceaimra

Syntactical analysis of total termination [chapter]

M. C. F. Ferreira, H. Zantema
1994 Lecture Notes in Computer Science  
In the first part we introduce a generalization of re cursive path order presenting a new proof of its well-foundedness without using Kruskal's theorem.  ...  In [5] we introduced the notion of total termination: basically terms are interpreted corn positionally in a total well-founded order, in such a way that rewriting chains map to descending chains.  ...  Let ZR denote the set of all partial orders over T(F) satisfying those conditions, and which is non empty by hypothesis.  ... 
doi:10.1007/3-540-58431-5_15 fatcat:rweki3okobf33l7utd7maqqbo4

Jumping and escaping: Modular termination and the abstract path ordering

Nachum Dershowitz
2012 Theoretical Computer Science  
Combinatorial commutation properties for reordering a sequence consisting of two kinds of steps, and for separating the well-foundedness of their combination into well-foundedness of each, are investigated  ...  generic, abstract version of the recursive path orderings. 1 These are the non-strongly-normalizing elements in R.  ...  We set out to prove the well-foundedness of a very abstract ordering that includes the usual path orderings as special cases.  ... 
doi:10.1016/j.tcs.2012.09.013 fatcat:eml7kpgvofaplbxqhbafyyhjn4

Termination in ACL2 Using Multiset Relations [chapter]

J. L. Ruiz-Reina, J. A. Alonso, M. J. Hidalgo, F. J. Martín-Mateos
2003 Applied Logic Series  
We prove this property in the ACL2 logic, and use it by functional instantiation in order to provide well-founded relations for the admissibility test of recursive functions.  ...  Every relation on a set A induces a relation on finite multisets over A; it can be shown that the multiset relation induced by a well-founded relation is also well-founded.  ...  non-zero powers of ω in its Cantor normal form, and the coefficients of the Cantor normal form are represented by the number of repetitions of the corresponding power of ω.  ... 
doi:10.1007/978-94-017-0253-9_9 fatcat:c5apat4qx5amvljyex4gq7pc3u

Finiteness is mu-ineffable

David Park
1976 Theoretical Computer Science  
It follows that finiteness is not expressible even by an infinite set of wffs of the mu-calculus, since this property holds for first-order logic, as is well-kno n (see, for exam Shoenfield [ $3).  ...  Nevertheless certain facts about non-deterministic schemas, e.g. that all possible execution sequences terminate, are not necessarily expressible in it (they are directly related to well-foundedness properties  ... 
doi:10.1016/0304-3975(76)90022-0 fatcat:5b4zscyugrc2vhvp5bpasi4oci

On Well-Founded and Recursive Coalgebras [chapter]

Jiří Adámek, Stefan Milius, Lawrence S. Moss
2020 Lecture Notes in Computer Science  
In addition, we present a new equivalent characterization of well-foundedness: a coalgebra is well-founded iff it admits a coalgebra-toalgebra morphism to the initial algebra.  ...  of all well-founded coalgebras.  ...  in (1.1) to the setting of recursion arising from well-foundedness as we find it in (1.2) .  ... 
doi:10.1007/978-3-030-45231-5_2 fatcat:x376nvmz75bfvekoy7gva4ivhm

Partizan Games in Isabelle/HOLZF [chapter]

Steven Obua
2006 Lecture Notes in Computer Science  
Finally, games (modulo equality) are added to Isabelle's numeric types by showing that they are an instance of the axiomatic type class of partially ordered abelian groups.  ...  A polymorphic type of sets that are not bigger than ZF sets facilitates this. We formalize the induction principle that Conway uses throughout his proofs about games, and prove its correctness.  ...  Stefan Berghofer told the author why (1) cannot work and caused him to look into the multiset order. Clemens Ballarin helped to prove the properties of the zunion operator.  ... 
doi:10.1007/11921240_19 fatcat:fggfhr5jzzfklk4hx6o6elj4eq

RELATIVE PREDICATIVITY AND DEPENDENT RECURSION IN SECOND-ORDER SET THEORY AND HIGHER-ORDER THEORIES

SATO KENTARO
2014 Journal of Symbolic Logic (JSL)  
hold in the context of subsystems of second order set theory where the universe V of sets is treated as the given totality (nor in the contexts of those of n+3-th order number or set theories, where the  ...  class of all n+2-th order objects is treated as the given totality).  ...  He would like to appreciate the hospitality of members of Logic and Theory Group at Institut für Informatik und angewandte Mathematik, Universität Bern, during his stay at which he obtained most results  ... 
doi:10.1017/jsl.2014.28 fatcat:7pwkx3k25zbbzowkj6afpuyls4

Agreement Theorems in Dynamic-Epistemic Logic

Cédric Dégremont, Oliver Roy
2012 Journal of Philosophical Logic  
We look at these results from a syntactic point of view, showing that neither well-foundedness nor common priors are expressible in a commonly used language, but that the static agreement result is finitely  ...  We do not restrict ourselves to the finite case, and show that in countable structures such results hold if and only if the underlying "plausibility ordering" is well-founded.  ...  We are also grateful to the referees of TARK, and to the participants at the Research Seminar in Philosophy of Linguistics and the workshop Formal Modeling in Social Epistemology, both at Tilburg University  ... 
doi:10.1007/s10992-012-9236-4 fatcat:uoq4ksesn5e23ban3uwtical3e

Agreement theorems in dynamic-epistemic logic

Cédric Dégremont, Olivier Roy
2009 Proceedings of the 11th Conference on Theoretical Aspects of Rationality and Knowledge - TARK '09  
We look at these results from a syntactic point of view, showing that neither well-foundedness nor common priors are expressible in a commonly used language, but that the static agreement result is finitely  ...  We do not restrict ourselves to the finite case, and show that in countable structures such results hold if and only if the underlying "plausibility ordering" is well-founded.  ...  We are also grateful to the referees of TARK, and to the participants at the Research Seminar in Philosophy of Linguistics and the workshop Formal Modeling in Social Epistemology, both at Tilburg University  ... 
doi:10.1145/1562814.1562829 dblp:conf/tark/DegremontR09 fatcat:ufe2dhxizre6dp3o4yvfkzrudi

Agreement Theorems in Dynamic-Epistemic Logic [chapter]

Cédric Dégremont, Olivier Roy
2009 Lecture Notes in Computer Science  
We look at these results from a syntactic point of view, showing that neither well-foundedness nor common priors are expressible in a commonly used language, but that the static agreement result is finitely  ...  We do not restrict ourselves to the finite case, and show that in countable structures such results hold if and only if the underlying "plausibility ordering" is well-founded.  ...  We are also grateful to the referees of TARK, and to the participants at the Research Seminar in Philosophy of Linguistics and the workshop Formal Modeling in Social Epistemology, both at Tilburg University  ... 
doi:10.1007/978-3-642-04893-7_9 fatcat:iyeoymyajbh4da3fnjh4sobu7a

Loop Summarization and Termination Analysis [chapter]

Aliaksei Tsitovich, Natasha Sharygina, Christoph M. Wintersteiger, Daniel Kroening
2011 Lecture Notes in Computer Science  
The practical efficiency of the approach is evaluated using a set of Windows device drivers.  ...  The algorithm relies on a library of abstract domains to discover well-founded transition invariants.  ...  Non-empty finite totally-ordered sets always have a least element and, therefore, T is well-founded.  ... 
doi:10.1007/978-3-642-19835-9_9 fatcat:kfa6ag3pp5bdnfuzdk23ispgsq
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