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Well-foundedness of term orderings
[chapter]

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. ...

##
###
Extensions to the Estimation Calculus
[chapter]

1999
*
Lecture Notes in Computer Science
*

Our calculus enables automatic proofs

doi:10.1007/3-540-48242-3_16
fatcat:aw243rxzz5heln6zk2f23pzobq
*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*...##
###
A proof assistant for symbolic model-checking
[chapter]

1993
*
Lecture Notes in Computer Science
*

It also provides help with checking the

doi:10.1007/3-540-56496-9_25
fatcat:z33vuw456jcd3kpalg5e4ete2a
*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. ...##
###
Verifying an Applicative ATP Using Multiset Relations
[chapter]

2001
*
Lecture Notes in Computer Science
*

We have carried out a mechanical proof

doi:10.1007/3-540-45654-6_47
fatcat:qkpblk2rxjhvlcgeckgceaimra
*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". ...##
###
Syntactical analysis of total termination
[chapter]

1994
*
Lecture Notes in Computer Science
*

In the first part we introduce a generalization

doi:10.1007/3-540-58431-5_15
fatcat:rweki3okobf33l7utd7maqqbo4
*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. ...##
###
Jumping and escaping: Modular termination and the abstract path ordering

2012
*
Theoretical Computer Science
*

Combinatorial commutation properties for reordering a sequence consisting

doi:10.1016/j.tcs.2012.09.013
fatcat:eml7kpgvofaplbxqhbafyyhjn4
*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. ...##
###
Termination in ACL2 Using Multiset Relations
[chapter]

2003
*
Applied Logic Series
*

We prove this property in the ACL2 logic, and use it by functional instantiation in

doi:10.1007/978-94-017-0253-9_9
fatcat:c5apat4qx5amvljyex4gq7pc3u
*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. ...##
###
Finiteness is mu-ineffable

1976
*
Theoretical Computer Science
*

It follows that finiteness is not expressible even by an infinite

doi:10.1016/0304-3975(76)90022-0
fatcat:5b4zscyugrc2vhvp5bpasi4oci
*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 ...##
###
On Well-Founded and Recursive Coalgebras
[chapter]

2020
*
Lecture Notes in Computer Science
*

In addition, we present a new equivalent characterization

doi:10.1007/978-3-030-45231-5_2
fatcat:x376nvmz75bfvekoy7gva4ivhm
*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) . ...##
###
Partizan Games in Isabelle/HOLZF
[chapter]

2006
*
Lecture Notes in Computer Science
*

Finally, games (modulo equality) are added to Isabelle's numeric types by showing that they are an instance

doi:10.1007/11921240_19
fatcat:fggfhr5jzzfklk4hx6o6elj4eq
*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. ...##
###
RELATIVE PREDICATIVITY AND DEPENDENT RECURSION IN SECOND-ORDER SET THEORY AND HIGHER-ORDER THEORIES

2014
*
Journal of Symbolic Logic (JSL)
*

hold in the context

doi:10.1017/jsl.2014.28
fatcat:7pwkx3k25zbbzowkj6afpuyls4
*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 ...##
###
Agreement Theorems in Dynamic-Epistemic Logic

2012
*
Journal of Philosophical Logic
*

We look at these results from a syntactic point

doi:10.1007/s10992-012-9236-4
fatcat:uoq4ksesn5e23ban3uwtical3e
*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 ...##
###
Agreement theorems in dynamic-epistemic logic

2009
*
Proceedings of the 11th Conference on Theoretical Aspects of Rationality and Knowledge - TARK '09
*

We look at these results from a syntactic point

doi:10.1145/1562814.1562829
dblp:conf/tark/DegremontR09
fatcat:ufe2dhxizre6dp3o4yvfkzrudi
*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 ...##
###
Agreement Theorems in Dynamic-Epistemic Logic
[chapter]

2009
*
Lecture Notes in Computer Science
*

We look at these results from a syntactic point

doi:10.1007/978-3-642-04893-7_9
fatcat:iyeoymyajbh4da3fnjh4sobu7a
*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 ...##
###
Loop Summarization and Termination Analysis
[chapter]

2011
*
Lecture Notes in Computer Science
*

The practical efficiency

doi:10.1007/978-3-642-19835-9_9
fatcat:kfa6ag3pp5bdnfuzdk23ispgsq
*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. ...
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