Almost forty years ago Richard Montague proposed to analyse natural language with the same tools as formal languages. In particular, he gave formal semantic analyses of several interesting fragments of English in terms of typed logic. This led to the development of Montague grammar as a particular style of formal analysis of natural language.

Provides computer science students and researchers with a firm background in lambda-calculus and combinators.

We propose a rudimentary formal framework for reasoning about recursion equations over inductively generated data. Our formalism admits all equational programs , and yet singles out none. While being simple, this framework has numerous extensions and applications. Here we lay out the basic concepts and definitions; show that the deductive power of our formalism is similar to that of Peano's Arithmetic; prove a strong normalization theorem; and exhibit a mapping from natural deduction derivations to an applied λ -calculus, à la (...) Curry–Howard, which provides a transparent proof of Gödel's result that the provably recursive functions of PA are definable by primitive recursion in finite types. Also of interest is the extent, uncommon among similar constructions, to which our mapping is oblivious to first order terms, including first order quantification and equality. Additional applications and extensions of the method will be presented in sequel papers. In particular, the methodology introduced here lends itself to systematic links between natural sub-formalisms and computational complexity classes. Since these sub-formalisms are largely transparent, allowing one to reason formally in the full system while leaving to automatic software tools the task of verifying that restrictions are complied with, the framework is particularly attractive for the development of Feasible Mathematics. (shrink)

Epistemic logic is the logic of knowledge, and dynamic epistemic logic is the logic of effects of communicative actions on the knowledge states of a set of agents. Typical communicative actions are making public announcements, passing private messages, revealing secrets, telling lies. This paper takes its starting point from the version of dynamic epistemic logic of [3], and demonstrates a tool that can be used for showing what goes on during a series of epistemic updates: the dynamic epistemic modelling tool (...) DEMO [10]. DEMO allows modelling epistemic updates, graphical display of update results, graphical display of action models, formula evaluation in epistemic models, and translation of dynamic epistemic formulas to PDL [23] formulas. DEMO is written in Haskell. This paper intends to demonstrate its use for calculating and visualizing the model transformations that take place during epistemic updating. (shrink)

An emerging standard for polymorphically typed, lazy, purely functional programming is Haskell, a language named after Haskell Curry. Haskell is based on (polymorphically typed) lambda calculus, which makes it an excellent tool for computational semantics.

The Lisp programming language is often described as the first functional programming language and also as an important early AI language. In the history of functional programming, however, it occupies a rather anomalous position, as the circumstances of its development do not fit well with the widely accepted view that functional languages have been developed through a theoretically-inspired project of deriving practical programming languages from the lambda calculus. This paper examines the origins of (...) Lisp in the early AI programming work of the mid-to-late 1950s, and in particular in the work of Allen Newell, Cliff Shaw and Herbert Simon. Their 1956 program, the Logic Theory Machine, introduced new ideas about data and program structures that were articulated in response to perceived limitations in existing programming technique. Later writers, notably John Backus, have described these features as constituting a “programming language style” distinct from the traditional style that preceded it. The paper examines the origins of the earlier style in practices of manual computation, analyses the key technical differences between it and the style first manifested in the Logic Theory Machine, and concludes that programming practice and experience play a large and underappreciated role in the development of programming styles and languages. (shrink)

We show the adequacy of axioms and proof rules for strict and lazy functional programs. Our basic logic comprises a huge part of what is common to the two styles of functional programming. The logic for call-by-value is obtained by adding the axiom that says that all variables are defined, whereas the logic for call-by-name is obtained by adding the axiom that postulates the existence of an undefined object for each type. To show the correctness of the (...) axiomatization we do not use denotational semantics and the adequacy of the evaluation of programs with respect to the semantics. Instead we use the standard term models based on call-by-value and call-by-name evaluation. We introduce a new method to prove on the syntactical level the monotonicity of the evaluation of functional programs with unbounded recursion. The direct method yields results concerning the proof-theoretic strength of the axiomatization. As a side result we obtain a syntactical proof of the context lemma for simply typed lambda terms with recursion. (shrink)

Dynamic epistemic logic is the logic of the effects of epistemic actions like making public announcements, passing private messages, revealing secrets, telling lies. This paper takes its starting point from the version of dynamic epistemic logic of [2], and demonstrates a tool that can be used for showing what goes on during a series of epistemic updates: the dynamic epistemic modelling tool DEMO [7, 9]. DEMO allows modelling epistemic updates, graphical display of update results, graphical display of action models, formula (...) evaluation in epistemic models, and translation of dynamic epistemic formulas to PDL [22] formulas. DEMO is written in Haskell. This paper intends to demonstrate its usefulness for visualizing the model transformations that take place during epistemic updating. (shrink)

This collection of current research on logic programming languages presents results from a three-year, ESPRIT-funded effort to explore the integration of the foundational issues of functional, logic, and object-oriented programming. It offers valuable insights into the fast-developing extensions of logic programming with functions, constraints, concurrency, and objects. Chapters are grouped according to the unifying themes of functional programming, constraint, logic programming, and object-oriented programming.

In 2006, in a special issue of this journal, several authors explored what they called the dual nature of artefacts. The core idea is simple, but attractive: to make sense of an artefact, one needs to consider both its physical nature—its being a material object—and its intentional nature—its being an entity designed to further human ends and needs. The authors construe the intentional component quite narrowly, though: it just refers to the artefact’s function, its being a means to realize a (...) certain practical end. Although such strong focus on functions is quite natural , I argue in this paper that an artefact’s intentional nature is not exhausted by functional considerations. Many non-functional properties of artefacts—such as their marketability and ease of manufacture—testify to the intentions of their users/designers; and I show that if these sorts of considerations are included, one gets much more satisfactory explanations of artefacts, their design, and normativity.Keywords: Artefacts; Dual Nature program; Function; Intentionality; Normativity. (shrink)

We study a hierarchy of Kalmàr elementary functions on integers based on a classification of LOOP programs of limited complexity, namely those in which the depth of nestings of LOOP commands does not exceed two. It is proved that -place functions in can be enumerated by a single function in , and that the resulting hierarchy of elementary predicates (i.e., functions with 0,1-values) is proper in that there are predicates that are not in . Along the way the rudimentary predicates (...) of Smullyan are classified as. (shrink)

As a result of these restrictions, an implementation of L [subscript lambda] does not need to implement full higher-order unification. Instead, an extension to first-order unification that respects bound variable names and scopes is all that is required. Such unification problems are shown to be decidable and to possess most general unifiers when unifiers exist. A unification algorithm and logic programming interpreter are described and proved correct. Several examples of using L[subscript lambda] as a meta-programming language are presented.

The issue of proper functioning of operative computing and the utility of program verification, both in general and of specific methods, has been discussed a lot. In many of those discussions, attempts have been made to take mathematics as a model of knowledge and certitude achieving, and accordingly infer about the suitable ways to handle computing. I shortly review three approaches to the subject, and then take a stance by considering social factors which affect the epistemic status of both mathematics (...) and computing. I use the analogy between mathematics and computing in reverse—that is to say, I consider operative computing as a form of making mathematics, and so attempt to learn from computing to mathematics in general. I conclude that mathematics engineering is a field to be both developed for practical improvement of doing mathematics and taken into consideration while philosophizing about mathematics as well. (shrink)

This study focuses on the influence of the work of Carl Stumpf on the thought of Karl Bühler. Our working hypothesis is based on the philosophical program that Bühler attributes to Stumpf and to which several of his works are largely indebted. It is divided into five parts. The first is intended to establish a relationship between Bühler and the School of Brentano to which Stumpf belongs. In the second, I show that Bühler became aware of Brentano's ideas and of (...) Stumpf's program during a stay at the Institute of Psychology of Berlin during the winter semester 1904-1905, and I briefly comment, in the third part, Bühler's references to the work of Stumpf and two of his books in which he defends Stumpf's program against his critics. After having established the solid knowledge that Bühler had of Stumpf's work, I outline, in the fourth part, the main aspects of this program and evaluate, in the fifth, how Bühler uses it in the field of sensory phenomena (gestalt). I conclude this study with several remarks on Stumpf's positive evaluation of the work of Bühler. (shrink)

The International Logic Programming Symposium is one of two major international conferences sponsored by the Association of Logic Programming. Both conferences are held annually. The theme for the 1995 conference was "Declarative Systems", particularly the integration of the logic programming, functional programming, and object-oriented programming paradigms.

Programmed cell death (PCD) in unicellular organisms is in some instances an altruistic trait. When the beneficiaries are clones or close kin, kin selection theory may be used to explain the evolution of the trait, and when the trait evolves in groups of distantly related individuals, group or multilevel selection theory is invoked. In mixed microbial communities, the benefits are also available to unrelated taxa. But the evolutionary ecology of PCD in communities is poorly understood. Few hypotheses have been offered (...) concerning the community role of PCD despite its far-reaching effects. The hypothesis we consider here is that PCD is a black queen. The Black Queen Hypothesis (BQH) outlines how public goods arising from a leaky function are exploited by other taxa in the community. Black Queen (BQ) traits are essential for community survival, but only some members bear the cost of possessing them, while others lose the trait In addition, BQ traits have been defined in terms of adaptive gene loss, and it is unknown whether this has occurred for PCD. Our conclusion is that PCD fulfils the two most important criteria of a BQ (leakiness and costliness), but that more empirical data are needed for assessing the remaining two criteria. In addition, we hold that for viewing PCD as a BQ, the original BQH needs to include social traits. Thus, despite some empirical and conceptual shortcomings, the BQH provides a helpful avenue for investigating PCD in microbial communities. (shrink)

The purpose of this randomized controlled study was to investigate the effects of a 12-week coordinative ability training program on adolescents’ cognitive functioning, using evaluation tests of visuospatial perception, attention, and working memory. We randomly assigned 60 public school students (14–15 years) to either an experimental coordinative abilities training (∼40 min twice/week) group (n= 30) or a control group (n= 30) who received general psycho-physical wellness training (∼40 min., twice a week). At baseline and after training we used two standardized (...) motor tests and a single cognitive measure (Corsi’s Block-tapping test) to assess students’ visuospatial perception, attention, and working memory. We found a significant Time x Group interaction for the Throwing and Catching Test and Corsi’s Block-Tapping test, reflecting a meaningful experimental group improvement (p< 0.001), and there were no significant pre-post changes found in the control group. Thus, a 12-week program of coordinative abilities was able to improve not only coordination skills but aspects of cognitive functioning relevant to academic achievement. (shrink)

Research regarding ethics programs represents an important segment of business ethics literature. In the last thirty years, scientific discourse on ethics programs has flourished. Numerous studies examined their functions, composition, application in organizational practice, and impact on employee ethical behavior and many other organizational variables. However, so far there has been no study that would comprehensively map this particular field. Given that, this paper aims to examine discourse on ethics programs in its complexity within business and management literature. Based on (...) a sophistically composed search protocol in the Scopus database, and after multiple rounds of checks, we extracted a final sample of 287 documents that matched the selection criteria. The sample was thoroughly analyzed by means of advanced bibliometric analytics tools. The results show the quantitative impact of ethics program literature via publication and citation metrics, a network of co-occurring themes and clusters of scientific inquiry, and the evolution of respective discourse over time. This detailed analysis results in a set of conclusions provided in the last part of the paper summarizing the quantitative performance and thematic scope of literature on ethics programs. (shrink)

We define a program size complexity function $H^\infty$ as a variant of the prefix-free Kolmogorov complexity, based on Turing monotone machines performing possibly unending computations. We consider definitions of randomness and triviality for sequences in ${\{0,1\}}^\omega$ relative to the $H^\infty$ complexity. We prove that the classes of Martin-Löf random sequences and $H^\infty$-random sequences coincide and that the $H^\infty$-trivial sequences are exactly the recursive ones. We also study some properties of $H^\infty$ and compare it with other complexity functions. In particular, $H^\infty$ (...) is different from $H^A$, the prefix-free complexity of monotone machines with oracle A. (shrink)

Just as war can be viewed as continuation of diplomacy using other means, computational semantics is continuation of logical analysis of natural language by other means. For a long time, the tool of choice for this used to be Prolog. In our recent textbook we argue (and try to demonstrate by example) that lazy functional programming is a more appropriate tool. In the talk we will lay out a program for computational semantics, by linking computational semantics to the (...) general analysis of procedures for social interaction. The talk will give examples of how Haskell can be used to begin carrying out this program. (shrink)

How to write a program in Haskell, and how to use the Haskell testing tools . . . QuickCheck is a tool written in the functional programming language Haskell that allows testing of specifications by means of randomly generated tests. QuickCheck is part of the standard Haskell library. Re-implementations of QuickCheck exist for many languages, including Ruby and Scheme. SmallCheck is a similar tool, different from QuickCheck in that it tests properties for all finitely many values of a (...) datatype up to some given depth, with progressive increase of depth. Haskell is a research language: many of the testing tools that were first developed for Haskell later find their way to other languages. These slides discuss QuickCheck (two versions), SmallCheck, and some work in progress. We end with some examples of Alloy specifications. (shrink)

Recently, connectionist models have been developed that seem to exhibit structuresensitive cognitive capacities without executing a program. This paper examines one such model and argues that it does execute a program. The argument proceeds by showing that what is essential to running a program is preserving the functional structure of the program. It has generally been assumed that this can only be done by systems possessing a certain temporalcausal organization. However, counterfactualpreserving functional architecture can be instantiated in other (...) ways, for example geometrically, which are realizable by connectionist networks. (shrink)

This study examined the recall of car and food advertisements within either a car or food television program to investigate the relationship between recall, program content, and viewer involvement. The participants, 92 sixth-form students, aged between 16–17 years, were randomly assigned to one of four conditions. As predicted, advertisements placed within a program of dissimilar content were recalled significantly better than if placed within a program of similar content. A gender bias in recall was found with females recalling female-orientated products (...) significantly better than males. Viewer-involvement ratings factored onto three factor clusters: enjoyable, cheerful, and humorous. Negative correlations were shown between cheerfulness and recall in the car program, and positive correlations were shown between cheerfulness and recall in the food program. Finally, implications of the results were considered. (shrink)