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Relations versus functions at the foundations of logic: . . .
 FORTHCOMING IN THE JOURNAL OF LOGIC AND COMPUTATION
"... Though Frege was interested primarily in reducing mathematics to logic, he succeeded in reducing an important part of logic to mathematics by defining relations in terms of functions. By contrast, Whitehead & Russell reduced an important part of mathematics to logic by defining functions in term ..."
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Though Frege was interested primarily in reducing mathematics to logic, he succeeded in reducing an important part of logic to mathematics by defining relations in terms of functions. By contrast, Whitehead & Russell reduced an important part of mathematics to logic by defining functions in terms of relations (using the definite description operator). We argue that there is a reason to prefer Whitehead & Russell’s reduction of functions to relations over Frege’s reduction of relations to functions. There is an interesting system having a logic that can be properly characterized in relational but not in functional type theory. This shows that relational type theory is more general than functional type theory. The simplification offered by Church in his functional type theory is an oversimplification: one can’t assimilate predication to functional application.
Coordination in Optimality Theory
 Nordic Journal of Linguistics
, 1999
"... I hereby certify that this dissertation is entirely the result of my own work, and that no material is included for which a degree has previously been conferred. I have faithfully, exactly and properly cited all sources made use of in the dissertation. ..."
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I hereby certify that this dissertation is entirely the result of my own work, and that no material is included for which a degree has previously been conferred. I have faithfully, exactly and properly cited all sources made use of in the dissertation.
Course Notes in Typed Lambda Calculus
, 1998
"... this paper is clearly stated, after recalling how the logical connectives can be explained in term of the Sheffer connective: "We are led to the idea, which at first glance certainly appears extremely bold of attempting to eliminate by suitable reduction the remaining fundamental notions, those ..."
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this paper is clearly stated, after recalling how the logical connectives can be explained in term of the Sheffer connective: "We are led to the idea, which at first glance certainly appears extremely bold of attempting to eliminate by suitable reduction the remaining fundamental notions, those of proposition, propositional function, and variable, from those contexts in which we are dealing with completely arbitrary, logical general propositions . . . To examine this possibility more closely and to pursue it would be valuable not only from the methodological point of view that enjoins us to strive for the greatest possible conceptual uniformity but also from a certain philosophic, or if you wish, aesthetic point of view."
The ChurchTuring Thesis as an Immature Form of the ZuseFredkin Thesis (More Arguments in Support of the “Universe as a Cellular Automaton” Idea)
"... In [1] we have shown a strong argument in support of the "Universe as a computer " idea. In the current work, we continue our exposition by showing more arguments that reveal why our Universe is not only "some kind of computer", but also a concrete computational ..."
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In [1] we have shown a strong argument in support of the &quot;Universe as a computer &quot; idea. In the current work, we continue our exposition by showing more arguments that reveal why our Universe is not only &quot;some kind of computer&quot;, but also a concrete computational model known as a &quot;cellular automaton&quot;.
Enumeration of generalized BCI lambdaterms
, 2013
"... We investigate the asymptotic number of elements of size n in a particular class of closed lambdaterms (socalled BCI(p)terms) which are related to axiom systems of combinatory logic. By deriving a differential equation for the generating function of the counting sequence we obtain a recurrence re ..."
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We investigate the asymptotic number of elements of size n in a particular class of closed lambdaterms (socalled BCI(p)terms) which are related to axiom systems of combinatory logic. By deriving a differential equation for the generating function of the counting sequence we obtain a recurrence relation which can be solved asymptotically. We derive differential equations for the generating functions of the counting sequences of other more general classes of terms as well: the class of BCK(p)terms and that of closed lambdaterms. Using elementary arguments we obtain upper and lowerestimates for the number of closed lambdaterms of size n. Moreover, a recurrence relation is derived which allows an efficient computation of the counting sequence. BCK(p)terms are discussed briefly. 1
unknown title
, 2004
"... A functional programming language for quantum computation with classical control ..."
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A functional programming language for quantum computation with classical control
From Search to Computation: Redundancy Criteria and Simplification at Work
"... The concept of redundancy and simplification has been an ongoing theme in Harald Ganzinger’s work from his first contributions to equational completion to the various variants of the superposition calculus. When executed by a theorem prover, the inference rules of these calculi usually generate a t ..."
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The concept of redundancy and simplification has been an ongoing theme in Harald Ganzinger’s work from his first contributions to equational completion to the various variants of the superposition calculus. When executed by a theorem prover, the inference rules of these calculi usually generate a tremendously growing search space. The redundancy and simplification concept is indispensable for cutting down this search space to a manageable size. For a number of subclasses of firstorder logic appropriate redundancy and simplification concepts even turn the superposition calculus into a decision procedure. Hence, the key to successfully applying firstorder theorem proving to a problem domain is to find those simplifications and redundancy criteria that fit this domain and can be effectively implemented. We present Harald Ganzinger’s work in the light of the simplification and redundancy techniques that have been developed for concrete problem areas. This includes a variant of contextual rewriting to decide a subclass of Euclidean geometry, ordered chaining techniques for ChurchRosser and priority queue proofs, contextual rewriting and historydependent complexities for the completion of conditional rewrite systems, rewriting with equivalences for theorem proving in set theory, soft typing for the exploration of sort information in the context of equations, and constraint inheritance for automated complexity analysis.