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A resolution principle for clauses with constraints
[chapter]

1990
*
Lecture Notes in Computer Science
*

The DFKI conducts application-oriented basic research in the field

doi:10.1007/3-540-52885-7_87
fatcat:u5qirrzlc5cbllzf2b27yaf6yq
*of*artificial intelligence and other related subfields*of*computer science. ... The overall goal is to construct systems with technical knowledge and common sense which -by using AI methods -implement a problem solution*for*a selected application area. ... Hence, as it contains*one*fewer excess literal, by the*induction*hypothesis there is a deduction*of*the empty A-*clause**for*this set. ...##
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Clausal Connection-Based Theorem Proving in Intuitionistic First-Order Logic
[chapter]

2005
*
Lecture Notes in Computer Science
*

We present a clausal connection calculus

doi:10.1007/11554554_19
fatcat:aacmbps255d7jo62s53bugoaxe
*for**first*-order intuitionistic logic. It extends the classical connection calculus by adding prefixes that encode the characteristics*of*intuitionistic logic. ... Our calculus is based*on*a clausal matrix characterisation*for*intuitionistic logic, which we prove correct and complete. The calculus was implemented by extending the classical prover leanCoP. ... Acknowledgements The author would like to thank Thomas Raths*for*providing the performance results*for*the listed classical and intuitionistic theorem proving systems. ...##
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Specifying coalgebras with modal logic

2001
*
Theoretical Computer Science
*

We propose to use modal logic as a logic

doi:10.1016/s0304-3975(00)00125-0
fatcat:4ebr5fvrpfddjbvocaraywymge
*for*coalgebras and discuss it in view*of*the work done*on*coalgebras as a semantics*of*object-oriented programming. ...*For*a certain kind*of*functor it is shown that the logic exactly captures the*notion**of*bisimulation and a complete calculus is given. Examples*of*veriÿcations*of*object properties are given. ... Acknowledgements I want to thank Martin R o iger*for*the good collaboration in preparing the version*of*the paper*for*this issue. ...##
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Matrix-Based Constructive Theorem Proving
[chapter]

2000
*
Applied Logic Series
*

We present a coherent account

doi:10.1007/978-94-015-9383-0_12
fatcat:psdwy6yocnhtve5oitvdf7lsxy
*of*matrix methods*for*constructive theorem proving and show how to extend them to*inductive*theorem proving by integrating rippling techniques into the unification process ... Bibel's connection method, originally developed*for*classical logic, has been extended to a variety*of*non-classical logics and used to control the creation*of*sequent proofs*for*interactive proof assistants ...*For*classical logic, we only need to consider quantifier-or*first*-order substitutions. A (*first*-*oder*) substitution σ Q (briefly σ) is a mapping from positions*of*type γ to terms. ...##
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Logical and Semantic Purity

2008
*
ProtoSociology
*

The

doi:10.5840/protosociology2008253
fatcat:cahe2ey6l5efpare5f3h6rprau
*first*is based*on*a view*of*Daniel Isaacson. ...*of*the natural numbers"*clause*he has in mind axioms, while by the second*clause*he has in mind theorems. ...##
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Inquisitive Semantics: Two Possibilities for Disjunction
[chapter]

2009
*
Lecture Notes in Computer Science
*

We introduce an inquisitive semantics

doi:10.1007/978-3-642-00665-4_8
fatcat:pibd42pkozd7tlqamtrc2ka76i
*for*a language*of*propositional logic, where the interpretation*of*disjunction is the source*of*inquisitiveness. ... The semantics comes with a new logical-pragmatical*notion*which judges and compares the compliance*of*responses to an initiative in inquisitive dialogue. ... The second*clause*holds trivially*for*assertions, since the antecedent can never be the case. The*first**clause*holds trivially*for*questions. ...##
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Towards a computation system based on set theory

1988
*
Theoretical Computer Science
*

An axiomatic theory

doi:10.1016/0304-3975(88)90115-6
fatcat:wrzdcjclh5gaxlpv7ve7zfewli
*of*sets and rules is formulated, which permits the use*of*sets as data structures and allaws nrles to operate*on*rules. numbers, or sets. ... Some related philosophical considerationson the*notions*oiset, type,and data structure aregiven in an appendix. ...*of*set theory (in particular*induction*) are to be*valid*. ...##
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Constructions, proofs and the meaning of logical constants

1983
*
Journal of Philosophical Logic
*

The meaning

doi:10.1007/bf00247187
fatcat:ejkflizf2fhg5me75tg5q5yota
*of*p is a proof*of*v(u) = 0*for*alI II, is understood*for**notions*v; in other words, we recognize a proof af an assertion*of*this form when we see*one*. ... The constructions which occur in the second*clauses*are*of*the sort (a), whereas in the*first*caluse*of*the implicationexplanation the construction is*of*the sort (b). ...##
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Proof Transformations for Evolutionary Formal Software Development
[chapter]

2002
*
Lecture Notes in Computer Science
*

These transformations are operationally motivated: how would

doi:10.1007/3-540-45719-4_30
fatcat:tm3npco76nasxabc73qicj2kv4
*one*patch the proofs*on*paper given a consistent transformation*for*the specification? ... The reference instantiation works*for*many practically relevant scenarios. Other instantiations can be based*on*the framework. ...*For**one**of*the calculus rules we need the*notion**of*a path in a development graph. ...##
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On the completeness of narrowing as the operational semantics of functional logic programming
[chapter]

1993
*
Lecture Notes in Computer Science
*

A declarative semantics

doi:10.1007/3-540-56992-8_14
fatcat:koaepjhtcreqva3yucpflvu5su
*for*these programs, which is based*on*applicative algebras over Scott domains, can be borrowed from Go&al 91]. ... We prove soundness and completeness*of*nite computations which solve some*equational*goal and nite segments*of*in nite computations which approach some in nite value in the limit. ... Proof: (N) and (S) are proved simultaneously by*induction**on*the structure*of*computations. We must consider*one*case*for*each rule*of*the narrowing calculus. ...##
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On novel facts

1988
*
Journal for General Philosophy of Science, Zeitschrift für allgemeine Wissenschaftstheorie
*

Zusammenfassung Das Problem, unter welchen Bedingungen eine Hypothese

doi:10.1007/bf01801335
fatcat:o65hyq2265ezlohn7knqe24ptq
*oder*Theorienmodifikation als methodologisch akzeptabel gilt, wird in der wissenschaftstheoretischen Tradition als die Frage des Ad-Hoc-Charakters ... Mit Hilfe dieser Kl~rungen wird unter anderem der Ad-hoc-Charakter der Lorentzschen Kontraktionshypothese sowie das Problem der Gleich-*oder*Verschiedenartigkeit yon Michelson-Mortey-und Kennedy-Thorndike-Experiment ... In the case*of*Boyle's law the ceteris-paribus-*clause*is only*valid*if no temperature changes occur. ...##
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Foundational nonuniform (Co)datatypes for higher-order logic

2017
*
2017 32nd Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)
*

Moreover, we derive (co)recusion and (co)

doi:10.1109/lics.2017.8005071
dblp:conf/lics/BlanchetteM0T17
fatcat:e6jjxy4c5rd6fa5yzq4acirk34
*induction*principles based*on*a weak variant*of*parametricity. ... They are often used to model the datatypes*of*languages with a nonstrict (lazy) evaluation strategy, such as Haskell, and they can be very convenient*for*some proving tasks. ... Acknowledgment: We thank Peter Lammich*for*pointing us to his work*on*finger trees and*for*formalizing Okasaki's construction*for*powerlists and Johannes Hölzl*for*explaining us Lean's support*for*nonuniform ...##
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Dedekind's Map-theoretic Period

2016
*
Philosophia Mathematica
*

In 1887-1894, Richard Dedekind explored a number

doi:10.1093/philmat/nkw010
fatcat:6o6xdliyl5gc3jeqp4kpcuvdyu
*of*ideas within the project*of*placing mappings at the very center*of*pure mathematics. ... to the work*of*other mathematicians. ... the principle*of**induction*is*valid**for*N. 30 As a matter*of*fact, everything is done via mappings and chains: 31 the elementary theory*of*finite and infinite sets, the theory*of*initial segments*of*N ...##
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Antirealism and the Roles of Truth
[chapter]

2004
*
Handbook of Epistemology
*

inspiration

doi:10.1007/978-1-4020-1986-9_11
fatcat:jglefav2yfbvpg23xu3byd7a2e
*for*much*of*the current work*on*semantical antirealism. ... meaning has to take, and, in particular, what role has to be played by the*notion**of*truth in such a theory. ...*clauses*. ...##
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Selective Conscientious Objection: Divine Will and Legislative Grace

1968
*
Virginia law review
*

His conscientious objector claim was raised

doi:10.2307/1071735
fatcat:cvcrmnsujbbnbpgf2flqg6gwyy
*for*the*first*time in a motion to dismiss an indictment brought against him*for*failure to report*for**induction*. ... In Peter it was held*valid**on*its face, in Jakobson*valid*as construed, and in Seeger invalid however construed. 40 United States v. ...
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