Lindstrom theorems for fragments of first-order logic

Lindstr\"om theorems characterize logics in terms of model-theoretic conditions such as Compactness and the L\"owenheim-Skolem property. Most existing characterizations of this kind concern extensions of first-order logic. But on the other hand, many logics relevant to computer science are fragments or extensions of fragments of first-order logic, e.g., k-variable logics and various modal logics. Finding Lindstr\"om theorems for these languages can be challenging, as most known techniques rely on coding arguments that seem to require the full expressive power of first-order logic. In this paper, we provide Lindstr\"om theorems for several fragments of first-order logic, including the k-variable fragments for k>2, Tarski's relation algebra, graded modal logic, and the binary guarded fragment. We use two different proof techniques. One is a modification of the original Lindstr\"om proof. The other involves the modal concepts of bisimulation, tree unraveling, and finite depth. Our results also imply semantic preservation theorems.Comment: Appears in Logical Methods in Computer Science (LMCS

The formal failure and social success of logic

Is formal logic a failure? It may be, if we accept the context-independent limits imposed by Russell, Frege, and others. In response to difficulties arising from such limitations I present a Toulmin-esque social recontextualization of formal logic. The results of my project provide a positive view of formal logic as a success while simultaneously reaffirming the social and contextual concerns of argumentation theorists, critical thinking scholars, and rhetoricians

P.B. Shelley's Poem Ozymandias in Russian Translations

The article presents a comparative analysis of Russian translations of P.B.Shelley's poem Ozymandias (1817), carried out by Ch. Vetrinsky, A.P. Barykova, K.D. Balmont, N. Minsky, V.Ya. Bryusov in 1890 - 1916. These translations fully reflect the peculiarities of the social and political, cultural and literary life in Russia of the late 19th - early 20th Centuries, namely weakening of the political system, growing of interest to the culture of Ancient Egypt, and strengthening of Neoromanticism in opposition to Naturalism in literature. In the process of the analysis, we used H. Smith's sonnet Ozymandias, P.B. Shelley's sonnet Ozymandias and its five Russian translations. The methods of historical poetics of A.N. Veselovsky, V.M. Zhirmunsky and provisions of the linguistic theory of translation of A.V. Fedorov were used. The article will be interesting for those studying literature, languages, philology

Singular and Plural Functions for Functional Logic Programming

Functional logic programming (FLP) languages use non-terminating and non-confluent constructor systems (CS's) as programs in order to define non-strict non-determi-nistic functions. Two semantic alternatives have been usually considered for parameter passing with this kind of functions: call-time choice and run-time choice. While the former is the standard choice of modern FLP languages, the latter lacks some properties---mainly compositionality---that have prevented its use in practical FLP systems. Traditionally it has been considered that call-time choice induces a singular denotational semantics, while run-time choice induces a plural semantics. We have discovered that this latter identification is wrong when pattern matching is involved, and thus we propose two novel compositional plural semantics for CS's that are different from run-time choice. We study the basic properties of our plural semantics---compositionality, polarity, monotonicity for substitutions, and a restricted form of the bubbling property for constructor systems---and the relation between them and to previous proposals, concluding that these semantics form a hierarchy in the sense of set inclusion of the set of computed values. We have also identified a class of programs characterized by a syntactic criterion for which the proposed plural semantics behave the same, and a program transformation that can be used to simulate one of them by term rewriting. At the practical level, we study how to use the expressive capabilities of these semantics for improving the declarative flavour of programs. We also propose a language which combines call-time choice and our plural semantics, that we have implemented in Maude. The resulting interpreter is employed to test several significant examples showing the capabilities of the combined semantics. To appear in Theory and Practice of Logic Programming (TPLP)Comment: 53 pages, 5 figure