Lawrence S. Moss

Lawrence S. Moss
Indiana University Bloomington | IUB · Department of Mathematics

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Publications (165)
Chapter
This chapter studies results whereby a set functor is lifted to other categories, paying attention to whether the initial algebra and terminal coalgebra structures also lift. For example, given a set functor F having a terminal coalgebra and a lifting on either complete partial orders and complete metric spaces, the terminal coalgebra can be equipp...
Chapter
Providing an in-depth treatment of an exciting research area, this text's central topics are initial algebras and terminal coalgebras, primary objects of study in all areas of theoretical computer science connected to semantics. It contains a thorough presentation of iterative constructions, giving both classical and new results on terminal coalgeb...
Chapter
This chapter takes the iterative construction of initial algebras into the transfinite, generalizing work in Chapters 2 and 4. It begins with a brief presentation of ordinals, cardinals, regular cardinals, and Zermelo’s Theorem: Monotone functions on chain-complete posets have least fixed points obtainable by iteration. When a category has colimits...
Chapter
Providing an in-depth treatment of an exciting research area, this text's central topics are initial algebras and terminal coalgebras, primary objects of study in all areas of theoretical computer science connected to semantics. It contains a thorough presentation of iterative constructions, giving both classical and new results on terminal coalgeb...
Chapter
Corecursive algebras are algebras that admit unique solutions of recursive equation systems. We study these and a generalization: completely iterative algebras. The terminal coalgebra turns out to be the initial corecursive algebra as well as the initial completely iterative algebra. Dually, the initial algebra is the initial (parametrically) recur...
Chapter
Providing an in-depth treatment of an exciting research area, this text's central topics are initial algebras and terminal coalgebras, primary objects of study in all areas of theoretical computer science connected to semantics. It contains a thorough presentation of iterative constructions, giving both classical and new results on terminal coalgeb...
Chapter
This chapter presents a number of sufficient conditions to guarantee that an endofunctor has an initial algebra or a terminal coalgebra. We generalize Kawahara and Mori’s notion of a bounded set functor and prove that for a cocomplete and co-well-powered category with a terminal object, every endofunctor bounded by a generating set has a terminal c...
Chapter
Providing an in-depth treatment of an exciting research area, this text's central topics are initial algebras and terminal coalgebras, primary objects of study in all areas of theoretical computer science connected to semantics. It contains a thorough presentation of iterative constructions, giving both classical and new results on terminal coalgeb...
Chapter
This chapter presents the limit-colimit coincidence in categories enriched either in complete partial orders or in complete metric spaces. This chapter thus works in settings where one has a theory of approximations of objects, either as joins of $\omega$-chains or as limits of Cauchy sequences, and with endofunctors preserving this structure. Ther...
Chapter
This chapter highlights connections of the book’s topics to structures used in all areas of mathematics. Cantor famously proved that no set can be mapped onto its power set. We present some analogous results for metric spaces and posets. On the category of topological spaces, we consider endofunctors built from the Vietoris endofunctor using produc...
Chapter
The theme of this chapter is the relation between the initial algebra for a set functor and the terminal coalgebra, assuming that both exist and that the endofunctor is non-trivial. We introduced a notion called pre-continuity. Pre-continuous set functors generalize finitary and continuous set functors. For such functors, the initial algebra and th...
Chapter
Well-founded coalgebras generalize well-foundedness for graphs, and they capture the induction principle for well-founded orders on an abstract level. Taylor’s General Recursion Theorem shows that, under hypotheses, every well-founded coalgebra is parametrically recursive. We give a new proof of this result, and we show that it holds for all set fu...
Chapter
The rational fixed point of an endofunctor is a fixed point which is in general different from its initial algebra and its terminal coalgebra. It collects precisely the behaviours of all ‘finite’ coalgebras of a given endofunctor. For sets, they are those with finitely many states. Examples of rational fixed points include regular languages, eventu...
Chapter
This chapter presents simple and reachable coalgebras and constructions of the simple quotient of a coalgebra and the reachable part of a pointed one. It introduces well-pointed coalgebras: those which are both reachable and simple. Well-pointed coalgebras constitute a coalgebraic formulation of minimality of state-based systems. For set functors p...
Chapter
Given an endofunctor F we can form various derived endofunctors whose initial algebras and terminal coalgebras are related to those of F. The most prominent example are coproducts of F with constant functors, yielding free F-algebras, cofree F-coalgebras, and free completely iterative F-algebras. An initial algebra exists for a composite functor FG...
Chapter
A set functor is an endofunctor on the category of sets. Although the topic of set functors is quite large, there are few if any chapter-length summaries directed to a researcher in the area of this book. This appendix collects the results on set functors that such a person ought to know, including the main preservation properties, such as preserva...
Chapter
Providing an in-depth treatment of an exciting research area, this text's central topics are initial algebras and terminal coalgebras, primary objects of study in all areas of theoretical computer science connected to semantics. It contains a thorough presentation of iterative constructions, giving both classical and new results on terminal coalgeb...
Chapter
This chapter discusses terminal coalgebras obtained by methods other than the finitary iteration that we saw in Chapter 3. One way is by taking a quotient of a weakly terminal coalgebra. Another is to use Worrell’s Theorem: the terminal coalgebra of a finitary set functor is obtainable as a limit, using a doubled form of infinite iteration. The cha...
Book
Providing an in-depth treatment of an exciting research area, this text's central topics are initial algebras and terminal coalgebras, primary objects of study in all areas of theoretical computer science connected to semantics. It contains a thorough presentation of iterative constructions, giving both classical and new results on terminal coalgeb...
Article
This paper is a contribution to neural network semantics, a foundational framework for neuro-symbolic AI. The key insight of this theory is that logical operators can be mapped to operators on neural network states. In this paper, we do this for a neural network learning operator. We map a dynamic operator [φ] to iterated Hebbian learning, a simple...
Preprint
Full-text available
We extract mathematical concepts from mathematical text using generative large language models (LLMs) like ChatGPT, contributing to the field of automatic term extraction (ATE) and mathematical text processing, and also to the study of LLMs themselves. Our work builds on that of others in that we aim for automatic extraction of terms (keywords) in...
Article
Full-text available
We build and study dynamic versions of epistemic logic. We study languages parameterized by an action signature that allows one to express epistemic actions such as (truthful) public announcements, completely private announcements to groups of agents, and more. The language 𝓛(Σ) is modeled on dynamic logic. Its sentence-building operations include...
Preprint
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The Vietoris space of compact subsets of a given Hausdorff space yields an endofunctor $\mathscr V$ on the category of Hausdorff spaces. Vietoris polynomial endofunctors on that category are built from $\mathscr V$, the identity and constant functors by forming products, coproducts and compositions. These functors are known to have terminal coalgeb...
Article
Full-text available
We present the logic of Hebbian learning, a dynamic logicwhose semantics1 are expressed in terms of a layered neuralnetwork learning via Hebb’s associative learning rule. Its lan-guage consists of modality Tφ (read “typically φ,” formalizedas forward propagation), conditionals φ ⇒ ψ (read “typi-cally φ are ψ”), as well as dynamic modalities [φ+]ψ (...
Preprint
Full-text available
We consider dynamic versions of epistemic logic as formulated in Baltag and Moss "Logics for epistemic programs" (2004). That paper proposed a logical language (actually families of languages parameterized by action signatures) for dynamic epistemic logic. It had been shown that validity in the language is Pi-1-1-complete, so there are no recursive...
Preprint
Full-text available
The Initial Algebra Theorem by Trnkov\'a et al. states, under mild but inevitable assumptions, that an endofunctor has an initial algebra provided it has a pre-fixed point. The proof crucially depends on transfinitely iterating the functor and in fact shows that, equivalently, the (transfinite) initial-algebra chain stops. We give a constructive pr...
Article
This paper explores relational syllogistic logics, a family of logical systems related to reasoning about relations in extensions of the classical syllogistic. These are all decidable logical systems. We prove completeness theorems and complexity results for a natural subfamily of relational syllogistic logics, parametrized by constructors for term...
Preprint
Despite the tremendous recent progress on natural language inference (NLI), driven largely by large-scale investment in new datasets (e.g., SNLI, MNLI) and advances in modeling, most progress has been limited to English due to a lack of reliable datasets for most of the world's languages. In this paper, we present the first large-scale NLI dataset...
Chapter
Full-text available
This paper studies fundamental questions concerning category-theoretic models of induction and recursion. We are concerned with the relationship between well-founded and recursive coalgebras for an endofunctor. For monomorphism preserving endofunctors on complete and well-powered categories every coalgebra has a well-founded part, and we provide a...
Article
This paper presents the most basic logics for reasoning about the sizes of sets that admit either the union of terms or the intersection of terms. That is, our logics handle assertions All x y and AtLeast x y, where x and y are built up from basic terms by either unions or intersections. We present a sound, complete, and polynomial-time decidable p...
Article
Do state-of-the-art models for language understanding already have, or can they easily learn, abilities such as boolean coordination, quantification, conditionals, comparatives, and monotonicity reasoning (i.e., reasoning about word substitutions in sentential contexts)? While such phenomena are involved in natural language inference (NLI) and go b...
Preprint
This paper studies fundamental questions concerning category-theoretic models of induction and recursion. We are concerned with the relationship between well-founded and recursive coalgebras for an endofunctor. For monomorphism preserving endofunctors on complete and well-powered categories every coalgebra has a well-founded part, and we provide a...
Preprint
We present a new logic-based inference engine for natural language inference (NLI) called MonaLog, which is based on natural logic and the monotonicity calculus. In contrast to existing logic-based approaches, our system is intentionally designed to be as lightweight as possible, and operates using a small set of well-known (surface-level) monotoni...
Article
Workshop on Logic, Language, Information and Computation (WoLLIC) was held in Bogotá, Colombia, 24–27 July 2018, in the Departamento de Matemáticas of the Universidad de los Andes. WoLLIC (http://wollic.org) is a series of workshops, which started in 1994 with the aim of fostering interdisciplinary research in pure and applied logic. The idea is to...
Preprint
Full-text available
Do state-of-the-art models for language understanding already have, or can they easily learn, abilities such as boolean coordination, quantification, conditionals, comparatives, and monotonicity reasoning (i.e., reasoning about word substitutions in sentential contexts)? While such phenomena are involved in natural language inference (NLI) and go b...
Preprint
This is the proceedings of the Seventeenth conference on Theoretical Aspects of Rationality and Knowledge, 17-19 July 2019, Institut de Recherche en Informatique de Toulouse (IRIT), Toulouse University Toulouse, France. The mission of the TARK conferences is to bring together researchers from a wide variety of fields, including Artificial Intellige...
Article
We add Most X are Y to the syllogistic logic of All X are Y and Some X are Y . We prove soundness, completeness, and decidability in polynomial time. Our logic has infinitely many rules, and we prove that this is unavoidable.
Preprint
This paper explores relational syllogistic logics, a family of logical systems related to reasoning about relations in extensions of the classical syllogistic. These are all decidable logical systems. We prove completeness theorems and complexity results for a natural subfamily of relational syllogistic logics, parametrized by constructors for term...
Article
This is a survey on fixed points of endofunctors, including initial algebras and terminal coalgebras. We also consider the rational fixed point, a canonical domain of behavior for finitely presentable systems. In addition to the basic existence theorems for fixed points, several new results are presented. For example, the Smyth–Plotkin theorem that...
Book
This book discusses major milestones in Rohit Jivanlal Parikh’s scholarly work. Highlighting the transition in Parikh’s interest from formal languages to natural languages, and how he approached Wittgenstein’s philosophy of language, it traces the academic trajectory of a brilliant scholar whose work opened up various new avenues in research. Thi...
Chapter
This paper presents a logical system in which various group-level epistemic actions are incorporated into the object language. That is, we consider the standard modeling of knowledge among a set of agents by multi-modal Kripke structures. One might want to consider actions that take place, such as announcements to groups privately, announcements wi...
Article
Full-text available
A majority digraph is a finite simple digraph $G=(V,\to)$ such that there exist finite sets $A_v$ for the vertices $v\in V$ with the following property: $u\to v$ if and only if "more than half of the $A_u$ are $A_v$". That is, $u\to v$ if and only if $ |A_u \cap A_v | > \frac{1}{2} \cdot |A_u|$. We characterize the majority digraphs as the digraphs...
Conference Paper
This paper presents a sound and complete proof system for the logical system whose sentences are of the form All X are Y, Some X are Y and Most X are Y, where we interpret these sentences on finite models, with the meaning of “most” being “strictly more than half.” Our proof system is syllogistic; there are no individual variables.
Book
Edited in collaboration with FoLLI, the Association of Logic, Language and Information this book constitutes the refereed proceedings of the 22nd Workshop on Logic, Language, Information and Computation, WoLLIC 2015, held in the campus of Indiana University, Bloomington, IN, USA in July 2015. The 14 contributed papers, presented together with 8 inv...
Conference Paper
Finitary endofunctors of locally presentable categories are proved to have equational presentations. Special attention is paid to the Hausdorff functor of non-empty compact subsets of a complete metric space.
Chapter
This chapter has three discussions related to one of Johan van Benthem’s longstanding interests, the areas of interaction of logic and linguistics. We review much of what is known on the landscape of syllogistic logics. These are logics which correspond to fragments of language. The idea in this area is to have complete and decidable systems. Next...
Conference Paper
We study finite state transduction of automatic and morphic sequences. Dekking [4] proved that morphic sequences are closed under transduction and in particular morphic images. We present a simple proof of this fact, and use the construction in the proof to show that non-erasing transductions preserve a condition called α-substitutivity. Roughly, a...
Article
Full-text available
We study finite state transduction of automatic and morphic sequences. Dekking proved that morphic sequences are closed under transduction and in particular morphic images. We present a simple proof of this fact, and use the construction in the proof to show that non-erasing transductions preserve a condition called alpha-substitutivity. Roughly, a...
Article
KeenanEdward L. and FaltzLeonard M.. Boolean semantics for natural language. Synthese language library, vol. 23. D. Reidel Publishing Company, Dordrecht, Boston, and Lancaster, 1985, xii + 387 pp. - Volume 52 Issue 2 - Lawrence S. Moss
Article
ParteeBarbara H., ter MeulenAlice, and WallRobert E.. Mathematical methods in linguistics. Studies in linguistics and philosophy, vol. 30. Kluwer Academic Publishers, Dordrecht, Boston, and London, 1990, xx + 663 pp. - Volume 57 Issue 1 - Lawrence S. Moss
Article
Full-text available
This paper is concerned with final coalgebra representations of fractal sets. The background to our work includes Freyd’s Theorem: the unit interval is a final coalgebra of a certain endofunctor on the category of bipointed sets. Leinster’s far-ranging generalization of Freyd’s Theorem is also a central part of the discussion, but we do not directl...
Article
The final coalgebra for the finite power-set functor was described by Worrell who also proved that the final chain converges in ω+ω steps. We describe the step ω as the set of saturated trees, a concept equivalent to the modally saturated trees introduced by K. Fine in the 1970s in his study of modal logic. And for the bounded power-set functors P...
Article
Full-text available
Terminal coalgebras for a functor serve as semantic domains for state-based systems of various types. For example, behaviors of CCS processes, streams, infinite trees, formal languages and non-well-founded sets form terminal coalgebras. We present a uniform account of the semantics of recursive definitions in terminal coalgebras by combining two id...
Article
Full-text available
For endofunctors of varieties preserving intersections, a new description of the final coalgebra and the initial algebra is presented: the former consists of all well-pointed coalgebras. These are the pointed coalgebras having no proper subobject and no proper quotient. The initial algebra consists of all well-pointed coalgebras that are well-found...
Article
Full-text available
We begin by discussing the history of quantum logic, dividing it into three eras or lives. The first life has to do with Birkhoff and von Neumann's algebraic approach in the 1930's. The second life has to do with attempt to understand quantum logic as logic that began in the late 1950's and blossomed in the 1970's. And the third life has to do with...
Article
This paper provides a foundation for the polarity marking technique introduced by David Dowty [3] in connection with monotonicity reasoning in natural language and in linguistic analyses of negative polarity items based on categorial grammar. Dowty’s work is an alternative to the better-known algorithmic approach first proposed by Johan van Benthem...
Conference Paper
For set functors preserving intersections, a new description of the final coalgebra and the initial algebra is presented: the former consists of all well-pointed coalgebras. These are the pointed coalgebras having no proper subobject and no proper quotient. And the initial algebra consists of all well-pointed coalgebras that are well-founded in the...
Article
Full-text available
We consider infinite sequences of symbols, also known as streams, and the decidability question for equality of streams defined in a restricted format. This restricted format consists of prefixing a symbol at the head of a stream, of the stream function `zip', and recursion variables. Here `zip' interleaves the elements of two streams in alternatin...
Conference Paper
This paper presents a sound and complete logical system whose atomic sentences are the equalities of recursive terms involving sets. There are two interpretations of this language: one makes use of non-wellfounded sets with finite transitive closure, and the other uses pointed finite graphs modulo bisimulation. Our logical system is a sequent-style...
Conference Paper
Full-text available
The aim of this tutorial is to present the area of coalgebra to people interested in the kinds of semantic modeling that is prominent at TARK. Coalgebra is a general study of a great many kinds of models, and these include type spaces and Kripke models, and many others. But the theory is not overly general, it is not a theory of absolutely everythi...
Article
This paper adds comparative adjectives to two systems of syllogistic logic. The comparatives are interpreted by transitive and irreflexive relations on the underlying domain. The main point is to obtain sound and complete axiomatizations of the valid formulas in the logics. KeywordsSyllogistic logic–Completeness–Adjectives–Transitive relations
Conference Paper
We combine ideas coming from several fields, including modal logic, coalgebra, and set theory. Modally saturated trees were introduced by K. Fine in 1975. We give a new purely combinatorial formulation of modally saturated trees, and we prove that they form the limit of the final ωop- chain of the finite power-set functor P f. From that, we derive...
Article
Full-text available
This article has two purposes. The first is to present a final coalgebra construction for finitary endofunctors on Set that uses a certain subset L* of the limit L of the first ω terms in the final sequence. L* is the set of points in L which arise from all coalgebras using their canonical morphisms into L, and it was used earlier for different pur...
Chapter
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Two of the main motivations for logic and (model-theoretic) semantics overlap in the sense that both subjects are concerned with representing features of natural language meaning and inference. At the same time, the two subjects have other motivations and so are largely separate enterprises. This paper returns to the topic of language and logic, pr...
Article
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This article provides sound and complete logical systems for several fragments of English which go beyond syllogistic logic in that they use verbs as well as other limited syntactic material: universally and existentially quantified noun phrases, building on the work of Nishihara, Morita and Iwata (1990, Systems and Computers in Japan, 21, 96–111);...
Conference Paper
Full-text available
Final coalgebras for a functor serve as semantic domains for state based systems of various types. For example, formal languages, streams, non-well-founded sets and behaviors of CCS processes form final coalgebras. We present a uniform account of the semantics of recursive definitions in final coalgebras by combining two ideas: (1) final coalgebras...
Conference Paper
This paper is a contribution to natural logic, the study of logical systems for linguistic reasoning. We construct a system with the following properties: its syntax is closer to that of a natural language than is first-order logic; it can faithfully represent simple sentences with standard quantifiers, subject relative clauses (a recursive constru...
Article
This paper provides a general account of the notion of recursive program schemes, studying both uninterpreted and interpreted solutions. It can be regarded as the category-theoretic version of the classical area of algebraic semantics. The overall assumptions needed are small indeed: working only in categories with “enough final coalgebras” we show...
Preprint
This paper provides a general account of the notion of recursive program schemes, studying both uninterpreted and interpreted solutions. It can be regarded as the category-theoretic version of the classical area of algebraic semantics. The overall assumptions needed are small indeed: working only in categories with "enough final coalgebras" we show...
Conference Paper
Full-text available
The goal of natural logic is to present and study logical systems for reasoning with sentences of (or which are reasonably close to) ordinary language. This paper explores simple systems of natural logic which make use of intersecting adjectives; these are adjectives whose interpretation does not vary with the noun they modify. Our project in this...
Article
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Dans leurs précédents travaux [Theor. Comput. Sci. 366, No. 1–2, 3–59 (2006; Zbl 1154.68041)], les auteurs ont proposé une théorie générale des schémas de programmes récursifs et de leurs solutions. Ces travaux généralisaient des approches plus anciennes, qui utilisaient les ensembles ordonnés ou les espaces métriques en offrant une théorie utilisa...
Chapter
Traditional syllogisms involve sentences of the following simple forms: All X are Y, Some X are Y, No X are Y; similar sentences with proper names as subjects, and identities between names. These sentences come with the natural semantics using subsets of a given universe, and so it is natural to ask about complete proof systems. Logical systems are...
Article
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The Aristotelian syllogistic cannot account for the validity of many inferences involving relational facts. In this paper, we investigate the prospects for providing a relational syllogistic. We identify several fragments based on (a) whether negation is permitted on all nouns, including those in the subject of a sentence; and (b) whether the subje...
Article
This is a corrigendum for our paper [S. Milius, L.S. Moss, The category theoretic solution of recursive program schemes, Theoret. Comput. Sci. 366 (2006) 3–59]. The main results are correct, but we offer some changes to the definitions and proofs concerning interpreted recursive program schemes.
Article
It is a truism that for a machine to have a useful access to memory or workspace, it must “know” where its input ends and its working memory begins. Most machine models separate input from memory explicitly, in one way or another. We are interested here in computational models which do not separate input from working memory. We study the situation...
Article
This chapter discusses the applications of modal logic in linguistics and provides a sophisticated view of modern interfaces between logic and natural language. Modal logic is known in linguistics for the light it throws on semantics; Richard Montague's use of higher-order modal logic for this purpose is widely considered to be the starting point o...
Article
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This paper obtains the weak completeness and decidability results for standard systems of modal logic using models built from formulas themselves. This line of work began with Fine (Notre Dame J. Form. Log. 16:229–237, 1975). There are two ways in which our work advances on that paper: First, the definition of our models is mainly based on the rela...
Chapter
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We present the main ideas behind a number of logical systems for rea- soning about points and sets that incorporate knowledge-theoretic ideas, and also the main results about them. Some of our discussions will be about applications of modal ideas to topology, and some will be on applications of topological ideas in modal logic, especially in episte...
Article
We prove that every functor on the category Meas of measurable spaces built from the identity and constant functors using products, coproducts, and the probability measure functor Δ has a final coalgebra. Our work builds on the construction of the universal Harsanyi type spaces by Heifetz and Samet and papers by Rößiger and Jacobs on coalgebraic mo...
Conference Paper
This talk describes work on one of the first applications of algebra to theoretical computer science, the study of recursive program schemes. I would like to put a lot of the past work in perspective and then to describe recent work by Stefan Milius and myself which reworks the classical theory of uninterpreted and interpreted recursive program sch...
Conference Paper
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This paper studies uniformity conditions for endofunctors on sets following Aczel [1], Turi [21], and others. The “usual” functors on sets are uniform in our sense, and assuming the Anti-Foundation Axiom AFA, a uniform functor H has the property that its greatest fixed point H * is a final coalgebra whose structure is the identity map. We propose a...
Article
This paper presents applied logic as a general research area, situating it in the broader intellectual world. It proposes a characterization of applied logic and attempts to say why the subject is interesting. It discusses the relation of applied logic with other trends in logic, computer science, and mathematics. Rather than present any technical...
Article
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Register machine programs provide explicit proofs of the sm n -Theorem, Kleene's Second Recursion Theorem, and Smullyan's Double Recur- sion Theorem. Thus these programs provide a pedagogically useful approach. We develop this topic from scratch, hence without appeal to the existence of universal programs, pairing, quotation, or any form of coding...
Chapter
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We construct logical languages which allow one to represent a variety of possible types of changes affecting the information states of agents in a multi-agent setting. We formalize these changes by defining a notion of epistemic program. The languages are two-sorted sets that contain not only sentences but also actions or programs. This is as in dy...
Conference Paper
Full-text available
This paper provides a general account of the notion of recursive program schemes, their uninterpreted and interpreted solutions, and related concepts. It can be regarded as the category-theoretic version of the classical area of algebraic semantics. The overall assumptions needed are small indeed: working only in categories with “enough final coalg...
Article
The articles in this part of this issue of the journal are a selection of the papers originally presented to the Fifth Workshop on Coalgebraic Methods in Computer Science. CMCS was held in April 2002, in Grenoble, France as a satellite conference of ETAPS. The conference proceedings were published in Electronic Notes in Theoretical Computer Science...
Article
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In dynamic epistemic logic and other fields, it is natural to consider relativiza- tion as an operator taking sentences to sentences. When using the ideas and methods of dynamic logic, one would like to iterate operators. This leads to iterated relativization. We are also concerned with the transitive closure operation, due to its connection to com...
Article
One of the interesting trends in theoretical computer science in recent years is the turn towards new application areas. It is not strange to see career shifts from complexity theory to cryptography, from type theory to security, from formal language theory to computational biology. The trend is reflected in journals as well. For example, the newly...
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§1. Introduction . Our understanding of Nature comes in layers, so should the development of logic. Classic logic is an indispensable part of our knowledge, and its interactions with computer science have recently dramatically changed our life. A new layer of logic has been developing ever since the discovery of quantum mechanics. G. D. Birkhoff an...
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This paper connects coalgebra with a long discussion in the foundations of game theory on the modeling of type spaces. We argue that type spaces are coalgebras, that universal type spaces are final coalgebras, and that the modal logics already proposed in the economic theory literature are closely related to those in recent work in coalgebraic moda...
Article
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This volume contains the Proceedings of the joint meeting of two conferences: the sixth conference on Formal Grammar and the seventh on Mathematics of Language. The meeting was held just prior to the European Summer School in Logic, Language, and Information in August 2001.FGMOL'01 provided a forum for the presentation of new and original research...
Article
We construct logical languages which allow one to represent a variety of possible types of changes affecting the information states of agents in a multi-agent setting. We formalize these changes by defining a notion of epistemic program. The languages are two-sorted sets that contain not only sentences but also actions or programs. This is as in dy...

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