A variant of realizability for Heyting arithmetic which validates Church’s thesis with uniqueness condition, but not the general form of Church’s thesis, was introduced by Lifschitz (Proc Am Math Soc 73:101–106, 1979). A Lifschitz counterpart to Kleene’s realizability for functions (in Baire space) was developed by van Oosten (J Symb Log 55:805–821, 1990). In that paper he also extended Lifschitz’ realizability to second order arithmetic. The objective here is to extend it to full intuitionistic (...) Zermelo–Fraenkel set theory, IZF. The machinery would also work for extensions of IZF with large set axioms. In addition to separating Church’s thesis with uniqueness condition from its general form in intuitionistic set theory, we also obtain several interesting corollaries. The interpretation repudiates a weak form of countable choice, ACω,ω, asserting that a countable family of inhabited sets of natural numbers has a choice function. ACω,ω is validated by ordinary Kleene realizability and is of course provable in ZF. On the other hand, a pivotal consequence of ACω,ω, namely that the sets of Cauchy reals and Dedekind reals are isomorphic, remains valid in this interpretation. Another interesting aspect of this realizability is that it validates the lesser limited principle of omniscience. (shrink)

V. Lifschitz defined in 1979 a variant of realizability which validates Church's thesis with uniqueness condition, but not the general form of Church's thesis. In this paper we describe an extension of intuitionistic arithmetic in which the soundness of Lifschitz' realizability can be proved, and we give an axiomatic characterization of the Lifschitz-realizable formulas relative to this extension. By a "q-variant" we obtain a new derived rule. We also show how to extend Lifschitz' (...) class='Hi'>realizability to second-order arithmetic. Finally we describe an analogous development for elementary analysis, with partial continuous application replacing partial recursive application. (shrink)

We develop a number of variants of Lifschitz realizability for $\mathbf {CZF}$ by building topological models internally in certain realizability models. We use this to show some interesting metamathematical results about constructive set theory with variants of the lesser limited principle of omniscience including consistency with unique Church’s thesis, consistency with some Brouwerian principles and variants of the numerical existence property.

F. Richman raised the question of whether the following principle of second order arithmetic is valid in intuitionistic higher order arithmetic $\mathbf{HAH}$: $\forall X\lbrack\forall x(x \in X \vee \neg x \in X) \wedge \forall Y(\forall x(x \in Y \vee \neg x \in Y) \rightarrow \forall x(x \in X \rightarrow x \in Y) \vee \forall x \neg(x \in X \wedge x \in Y)) \rightarrow \exists n\forall x(x \in X \rightarrow x = n)\rbrack$, and if not, whether assuming Church's Thesis CT and (...) Markov's Principle MP would help. Blass and Scedrov gave models of $\mathbf{HAH}$ in which this principle, which we call RP, is not valid, but their models do not satisfy either CT or MP. In this paper a realizability topos Lif is constructed in which CT and MP hold, but RP is false. (It is shown, however, that $RP$ is derivable in $\mathbf{HAH} + \mathrm{CT} + \mathrm{MP} + \mathrm{ECT}_0$, so RP holds in the effective topos.) Lif is a generalization of a realizability notion invented by V. Lifschitz. Furthermore, Lif is a subtopos of the effective topos. (shrink)

A belief in a firm correspondence between objects, ideas, and their representation in language pervaded the works of Anne Robert Jacques Turgot

(1727–1781) in 1750. This conviction is particularly manifest in Turgot’s sharp critique of Berkeley’s philosophical system and his remarks on Maupertuis’s reconstruction of the origin of language. During the 1750s Turgot’s epistemological views underwent a change, apparent in two of his contributions to the Encyclopédie: the entries Existence and Étymologie (1756). These articles included a reassessment of Berkeleyan immaterialism, facing (...) an ultimate crisis of definition and representation. A similar development may be traced in contemporary works by Condillac and Diderot. Turgot’s Encyclopédie entries also envisaged a new science, an archeology of the human mind aided by the examination of linguistic development and change. This entailed the scientific verification of conjectures in any historical account of ideas, turning etymological

and psychological inquiries into what Turgot termed ‘experimental metaphysics’. (shrink)

Jean-Jacques Rousseau has been cast as a champion of Enlightenment and a beacon of Romanticism, a father figure of radical revolutionaries and totalitarian dictators alike, an inventor of the modern notion of the self, and an advocate of stern ancient republicanism. Engaging with Rousseau treats his writings as an enduring topic of debate, examining the diverse responses they have attracted from the Enlightenment to the present. Such notions as the general will were, for example, refracted through very different prisms during (...) the struggle for independence in Latin America and in social conflicts in Eastern Europe, or modified by thinkers from Kant to contemporary political theorists. Beyond Rousseau's ideas, his public image too travelled around the world. This book examines engagement with Rousseau's works as well as with his self-fashioning; especially in turbulent times, his defiant public identity and his call for regeneration were admired or despised by intellectuals and political agents. (shrink)

Knowledge representation, which lies at the core of artificial intelligence, is concerned with encoding knowledge on computers to enable systems to reason automatically. The aims are to help readers make their computer smarter, handle qualitative and uncertain information, and improve computational tractability.

This is an expository article about the solution to the frame problem proposed in 1980 by Raymond Reiter. For years, his “frame default” remained untested and suspect. But developments in some seemingly unrelated areas of computer science—logic programming and satisfiability solvers—eventually exonerated the frame default and turned it into a basis for important applications.

What is the role of language in human cognition? Could we attain self-consciousness and construct our civilisation without language? Such were the questions at the basis of eighteenth-century debates on the joint evolution of language, mind, and culture. Language and Enlightenment highlights the importance of language in the social theory, epistemology, and aesthetics of the Enlightenment. While focusing on the Berlin Academy under Frederick the Great, Avi Lifschitz situates the Berlin debates within a larger temporal and geographical framework. He (...) argues that awareness of the historicity and linguistic rootedness of all forms of life was a mainstream Enlightenment notion rather than a feature of the so-called 'Counter-Enlightenment'. -/- Enlightenment authors of different persuasions investigated whether speechless human beings could have developed their language and society on their own. Such inquiries usually pondered the difficult shift from natural signs like cries and gestures to the artificial, articulate words of human language. This transition from nature to artifice was mirrored in other domains of inquiry, such as the origins of social relations, inequality, the arts and the sciences. By examining a wide variety of authors - Leibniz, Wolff, Condillac, Rousseau, Michaelis, and Herder, among others - Language and Enlightenment emphasises the open and malleable character of the eighteenth-century Republic of Letters. The language debates demonstrate that German theories of culture and language were not merely a rejection of French ideas. New notions of the genius of language and its role in cognition were constructed through a complex interaction with cross-European currents, especially via the prize contests at the Berlin Academy. (shrink)

Eighteenth-century Epicureanism is often viewed as radical, anti-religious, and politically dangerous. But to what extent does this simplify the ancient philosophy and underestimate its significance to the Enlightenment? Through a pan-European analysis of Enlightenment centres from Scotland to Russia via the Netherlands, France and Germany, contributors argue that elements of classical Epicureanism were appropriated by radical and conservative writers alike. They move beyond literature and political theory to examine the application of Epicurean ideas in domains as diverse as physics, natural (...) law, and the philosophy of language, drawing on the work of both major figures (Diderot, Helvétius, Smith and Hume) and of lesser-known but important thinkers (Johann Jacob Schmauss and Dmitrii Anichkov). -/- Table of Contents -/- Neven Leddy and Avi S. Lifschitz, Epicurus in the Enlightenment: an introduction -/- Elodie Argaud, Bayle’s defence of Epicurus: the use and abuse of Malebranche’s Méditations chrétiennes -/- Hans W. Blom, The Epicurean motif in Dutch notions of sociability in the seventeenth century -/- Thomas Ahnert, Epicureanism and the transformation of natural law in the early German Enlightenment -/- Charles T. Wolfe, A happiness fit for organic bodies: La Mettrie’s medical Epicureanism -/- Natania Meeker, Sexing Epicurean materialism in Diderot -/- Pierre Force, Helvétius as an Epicurean political theorist -/- Andrew Kahn, Epicureanism in the Russian Enlightenment: Dmitrii Anichkov and atomic theory -/- Matthew Niblett, Man, morals and matter: Epicurus and materialist thought in England from John Toland to Joseph Priestley -/- James A. Harris, The Epicurean in Hume -/- Neven Leddy, Adam Smith’s critique of Enlightenment Epicureanism -/- Avi S. Lifschitz, The Enlightenment revival of the Epicurean history of language and civilisation -/- Bibliography -/- Index. (shrink)

cuted actions. It has been applied to several challenge problems in the theory of commonsense knowledge. We study the relationship between this formalism and other work on nonmonotonic reasoning and knowl-.

Felicitous models were defined by Kit Fine in 1987 for the purpose of describing the semantics of negation in the programming language Prolog. They are often referred to as stable models, or answer sets. Years later, sophisticated software systems for generating answer sets were designed, and they became the basis of a new programming paradigm, called answer set programming. That programming method is used now for solving computational problems in many areas of science and technology. This chapter traces the early (...) history of felicitous models and the ways in which that idea contributed to computer science. (shrink)

This book constitutes the refereed proceedings of the 20th International Conference on Logic Programming, ICLP 2004, held in Saint-Malo, France in September 2004. The 28 revised full papers and 16 poster papers presented together with 2 invited papers were carefully reviewed and selected from 70 submissions. The papers are organized in topical sections on program analysis, constraints, alternative programming paradigms, answer set programming, and implementation.

In a fluent, clear, and lively style this translation by two of Maslov's junior colleagues brings the work of the late Soviet scientist S. Yu. Maslov to a wider audience. Maslov was considered by his peers to be a man of genius who was making fundamental contributions in the fields of automatic theorem proving and computational logic. He published little, and those few papers were regarded as notoriously difficult. This book, however, was written for a broad audience of readers and (...) describes elegant examples of applications in such fields as computer science, artificial intelligence, operations research, economic modeling, and biological modeling, among others. The book also brings to light the work by the American mathematician E. L. Post, which inspired Maslov's own work in the development of a general theory and which has been long neglected by mathematicial logicians and systems theorists in the United States. The book's first chapter introduces the Rules of the Game. Part I, Mathematics of Calculi, covers E. L. Post's canonical systems, deductive systems and algorithms, and probabilistic calculi and deductive information. Part II, Horizonal Modeling, takes up a "toy" economy, the calculi of technological possibilities, and the development of rules. Part III, Vertical Modeling, deals with the topics of "to fight and to search" and the consequences of the asymmetry of cognitive mechanisms. Vladimir Lifschitz is affiliated with the Department of Computer Science at Stanford University, and Michael Gelfond with the Department of Electrical Engineering and Computer Science at the University of Texas, El Paso. Theory of Deductive Systems and Its Applicationsis included in the Foundation of Computing Series, edited by Michael Garey. (shrink)

Answer set programming (ASP) is a form of declarative programming oriented towards difficult search problems. As an outgrowth of research on the use of nonmonotonic reasoning in knowledge representation, it is particularly useful in knowledge-intensive applications. ASP programs consist of rules that look like Prolog rules, but the computational mechanisms used in ASP are different: they are based on the ideas that have led to the creation of fast satisfiability solvers for propositional logic.

“Toy worlds” involving actions, such as the blocks world and the Missionaries and Cannibals puzzle, are often used by researchers in the areas of commonsense reasoning and planning to illustrate and test their ideas. We would like to create a database of generalpurpose knowledge about actions that encodes common features of many action domains of this kind, in the same way as abstract algebra and topology represent common features of specific number systems. This paper is a report on the first (...) stage of this project—the design of an action description language in which this database will be written. The new language is an extension of the action language C+. Its main distinctive feature is the possibility of referring to other action descriptions in the definition of a new action domain. (shrink)

This is a review of some of the definitions of the concept of a stable model that have been proposed in the literature. These definitions are equivalent to each other, at least when applied to traditional Prologstyle programs, but there are reasons why each of them is valuable and interesting. A new characterization of stable models can suggest an alternative picture of the intuitive meaning of logic programs; or it can lead to new algorithms for generating stable models; or it (...) can work better than others when we turn to generalizations of the traditional syntax that are important from the perspective of answer set programming; or it can be more convenient for use in proofs; or it can be interesting simply because it demonstrates a relationship between seemingly unrelated ideas. (shrink)

From the late seventeenth century to the middle of the eighteenth, an important shift occurred in attitudes to the arbitrariness of the first human words. While authors such as Locke and Pufendorf emphasized linguistic arbitrariness and human liberty, mid-eighteenth-century thinkers highlighted the natural aspects of language and the limited scope of freedom and reason. This change is linked to the contemporary view of the cultural world as a natural artifice, strongly molded by social and environmental factors. The article highlights hitherto (...) neglected similarities between Leibniz’s ideas on language and mid-eighteenth-century theories, by contrast to the usual focus on Locke. (shrink)

In a recent paper, Ferraris, Lee and Lifschitz conjectured that the concept of a stable model of a first-order formula can be used to treat some answer set programming expressions as abbreviations. We follow up on that suggestion and introduce an answer set programming language that defines the mean- ing of counting and choice by reducing these constructs to first-order formulas. For the new language, the concept of a safe program is defined, and its semantic role is investigated. We (...) compare the new language with the concept of a disjunc- tive program with aggregates introduced by Faber, Leone and Pfeifer, and discuss the possibility of implementing a frag- ment of the language by translating it into the input language of the answer set solver DLV. The language is also compared with cardinality constraint programs defined by Syrjänen. (shrink)

(Click here for selected papers published before 1996, and here for papers published after 2000.) V. Lifschitz, Foundations of logic programming ," in Principles of Knowledge Representation , CSLI Publications, 1996, pp. 69-127. E. Giunchiglia, N. Kartha and V. Lifschitz, Representing action: indeterminacy and ramifications ," Artificial Intelligence , Vol. 95, 1997, pp. 409-443. V. Lifschitz, On the logic of causal explanation ," Artificial Intelligence , Vol. 96, 1997, pp. 451-465. V. Lifschitz, Two components of an (...) action language ," Annals of Mathematics and Artificial Intelligence , Vol. 21, 1997, pp. 305-320. V. Lifschitz, Situation calculus and causal logic ," in Proceedings of the Sixth International Conference on Principles of Knowledge Representation and Reasoning, 1998, pp. 536-646. (shrink)

(Click here for the papers published between 1996 and 2000, and here for more recent papers.) V. Lifschitz, On the semantics of STRIPS ," in: Reasoning about Actions and Plans , 1987, pp. 1-9. M. Gelfond and V. Lifschitz, The stable model semantics for logic programming ," in Logic Programming: Proceedings of the Fifth International Conference and Symposium , 1988, pp. 1070-1080.

This book constitutes the refereed proceedings of the 7th International Conference on Logic Programming and Nonmonotonic Reasoning, LPNMR 2004, held in Fort Lauderdale, Florida, USA in January 2004. The 24 revised full papers presented together with 8 system descriptions were carefully reviewed and selected for presentation. Among the topics addressed are declarative logic programming, nonmonotonic reasoning, knowledge representation, combinatorial search, answer set programming, constraint programming, deduction in ontologies, and planning.

In this article Johann David Michaelis’s views of language and translation are juxtaposed with his own experience as a translated and translating author, especially with regard to the translations of his prize essay on the reciprocal influence of language and opinions (1759). Its French version originated in a close collaboration with the translators, while the pirated English edition was anonymously translated at second hand. The article reconstructs Michaelis’s relationship with the French translators and his renouncement of the English version, publicly (...) condemned in London by Robert Lowth at the author’s request. These two processes represent different contemporary modes of translation and shed new light on emerging theories of linguistic and cultural transfer. (shrink)

In July 1759 the French philosopher Andre´ Pierre Le Guay de Prémontval (1716-1764) published in Berlin a diatribe against the excessive and incorrect use of French in the Prussian capital. Far from being a mere guide to linguistic style, the Préservatif contre la corruption de la langue françoise generated a heated debate, attested by an official threat to ban its publication. The personal animosity between Prémontval and the perpetual secretary of the Berlin Academy, Jean Henri Samuel Formey (1711-1797) was amply (...) demonstrated over the pages of the Préservatif, offering a rare insight into the complex web of social and intellectual tensions in mid eighteenth-century Berlin and its Academy of Sciences. At stake were the social status and the philosophical outlook of local Huguenots, compared to that of French philosophers who were granted asylum in Prussia by Frederick II. The debate also concerned the issues of academic freedom in an absolutist regime, the material production and distribution of texts, conduct and etiquette in the Republic of Letters and the formation of group identities in eighteenth-century Germany. Drawing on manuscripts preserved in Berlin, Göttingen and Krakow, this article traces the development of the controversy and the reception of Prémontval’s work by both French- and German- writing authors at the Berlin Academy and beyond its confines. (shrink)

in Handbook of Knowledge representation, Elsevier, 2008.

The Epicurean account of the origin of language appealed to eighteenth-century thinkers who tried to reconcile a natural history of language with

the biblical account of Adamic name-giving. As a third way between Aristotelian linguistic conventionality and what was perceived as a Platonic supernatural congruence between words and things, Epicurus’

theory allowed for a measure of contingency to emerge in the evolution of initially natural signs. This hypothesis was taken up by authors as different from one another as Leibniz, Vico, Condillac and (...) Mendelssohn. By integrating the Epicurean account of language into their own theories, however, these authors also revived the tensions inherent in the ancient thesis and had to confront the ensuing difficulties in innovative ways. (shrink)

Nonmonotonic causal logic is a knowledge representation language designed for describing domains that involve actions and change. The process of literal completion, similar to program completion familiar from the theory of logic programming, can be used to translate some nonmonotonic causal theories into classical logic. Its applicability is restricted, however, to theories that deal with truth-valued fluents, represented by predicate symbols. In this note we introduce functional completion—a more general process that can be applied to causal theories in which fluents (...) are treated as functions. (shrink)

This paper is motivated by the idea of interaction between two directions of research in knowledge representation: the design of action description languages and the development of libraries of reusable, general-purpose knowledge components. Writing an action description that characterizes actions in terms of their effects, as common today, can be compared to writing a program that does not use standard subroutines. We conjecture that a library of standard descriptions for a number of “basic” actions can facilitate writing, understanding and modifying (...) action descriptions. In this paper, we take some steps towards determining how such a library, written in the action language C+, can be used. When using an instance of a library action description, we relate the library constants to the domain-specific constants by providing definitions. Therefore, a theory of explicit definitions in C+ is developed. To illustrate the use of the library, we show how the action PushBox in the Monkey and Bananas domain can be described as a special case of the “library action” Move. (shrink)

The language of nonmonotonic causal theories, defined by Norman McCain and Hudson Turner, is an important formalism for representing properties of actions. For causal theories of a special kind, called definite, a simple translation into the language of logic programs under the answer set semantics is available. In this paper we define a similar translation for causal theories of a more general form, called al-.

Natural sociability and the basic features of human nature stood at the centre of Thomas Abbt's confrontation with conjectural history, the popular eighteenth-century mode of reconstructing the evolution of human culture. Abbt (1738–1766) criticised conjectural histories due to their arbitrary character, and opted for a synthetic approach consisting of both sacred and secular history. He suggested that the anthropology of Genesis should be accepted as the starting point for a conjectural history, since it left ample room for further questions and (...) speculations. Yet his own perspective on human nature and its evolution remained naturalistic, as attested by his divergent interpretations of the confusion of tongues at Babel. Attempting to shed new light on the lesser-known elements of Abbt's work, the essay links his views on the Bible and conjectural history to his debate with Moses Mendelssohn over the constitution and destination of man. In this debate, both Mendelssohn and Abbt dealt with the contemporary controversy over the natural or artificial character of sociability, self-interest, and fellow-feeling. (shrink)

affects the collection of answer sets. In particular, it is useful to be able to describe the effects of adding definitions to a program with nested expressions, in view of the relation of this class of programs to the input language of the answer set programming system sMonELs. In this..

be irrelevant for achieving the given goal. We make this idea precise by defining, for an action description in language C+, when a subset of its..