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### A resolution principle for clauses with constraints [chapter]

Hans-Jürgen Bürckert
1990 Lecture Notes in Computer Science
The DFKI conducts application-oriented basic research in the field 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.  ...

### Clausal Connection-Based Theorem Proving in Intuitionistic First-Order Logic [chapter]

Jens Otten
2005 Lecture Notes in Computer Science
We present a clausal connection calculus 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.  ...

### Specifying coalgebras with modal logic

Alexander Kurz
2001 Theoretical Computer Science
We propose to use modal logic as a logic 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.  ...

### Matrix-Based Constructive Theorem Proving [chapter]

Christoph Kreitz, Jens Otten, Stephan Schmitt, Brigitte Pientka
2000 Applied Logic Series
We present a coherent account 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.  ...

### Logical and Semantic Purity

Andrew Arana
2008 ProtoSociology
The 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.  ...

### Inquisitive Semantics: Two Possibilities for Disjunction [chapter]

Jeroen Groenendijk
2009 Lecture Notes in Computer Science
We introduce an inquisitive semantics 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.  ...

### Towards a computation system based on set theory

Michael J. Beeson
1988 Theoretical Computer Science
An axiomatic theory 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.  ...

### Constructions, proofs and the meaning of logical constants

G�ran Sundholm
1983 Journal of Philosophical Logic
The meaning 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).  ...

### Proof Transformations for Evolutionary Formal Software Development [chapter]

Axel Schairer, Dieter Hutter
2002 Lecture Notes in Computer Science
These transformations are operationally motivated: how would 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.  ...

### On the completeness of narrowing as the operational semantics of functional logic programming [chapter]

Juan Carlos González-Moreno, María Teresa Hortalá-González, Mario Rodríguez-Artalejo
1993 Lecture Notes in Computer Science
A declarative semantics 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.  ...

### On novel facts

Martin Carrier
1988 Journal for General Philosophy of Science, Zeitschrift für allgemeine Wissenschaftstheorie
Zusammenfassung Das Problem, unter welchen Bedingungen eine Hypothese 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.  ...

### Foundational nonuniform (Co)datatypes for higher-order logic

Jasmin Christian Blanchette, Fabian Meier, Andrei Popescu, Dmitriy Traytel
2017 2017 32nd Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)
Moreover, we derive (co)recusion and (co)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  ...

### Dedekind's Map-theoretic Period

José Ferreirós
2016 Philosophia Mathematica
In 1887-1894, Richard Dedekind explored a number 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  ...

### Antirealism and the Roles of Truth [chapter]

Göran Sundholm
2004 Handbook of Epistemology
inspiration 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.  ...

### Selective Conscientious Objection: Divine Will and Legislative Grace

Hugh C. Macgill
1968 Virginia law review
His conscientious objector claim was raised 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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