A simple sequent calculus for nominal logic

Nominal logic is a variant of first-order logic that provides support for reasoning about bound names in abstract syntax. A key feature of nominal logic is the new-quantifier, which quantifies over fresh names (names not appearing in any values considered so far). Previous attempts have been made to develop convenient rules for reasoning with the new-quantifier, but we argue that none of these attempts is completely satisfactory. In this article we develop a new sequent calculus for nominal logic in which the rules for the new- quantifier are much simpler than in previous attempts. We also prove several structural and metatheoretic properties, including cut-elimination, consistency, and equivalence to Pitts' axiomatization of nominal logic

A Rational Deconstruction of Landin's SECD Machine with the J Operator

Landin's SECD machine was the first abstract machine for applicative expressions, i.e., functional programs. Landin's J operator was the first control operator for functional languages, and was specified by an extension of the SECD machine. We present a family of evaluation functions corresponding to this extension of the SECD machine, using a series of elementary transformations (transformation into continu-ation-passing style (CPS) and defunctionalization, chiefly) and their left inverses (transformation into direct style and refunctionalization). To this end, we modernize the SECD machine into a bisimilar one that operates in lockstep with the original one but that (1) does not use a data stack and (2) uses the caller-save rather than the callee-save convention for environments. We also identify that the dump component of the SECD machine is managed in a callee-save way. The caller-save counterpart of the modernized SECD machine precisely corresponds to Thielecke's double-barrelled continuations and to Felleisen's encoding of J in terms of call/cc. We then variously characterize the J operator in terms of CPS and in terms of delimited-control operators in the CPS hierarchy. As a byproduct, we also present several reduction semantics for applicative expressions with the J operator, based on Curien's original calculus of explicit substitutions. These reduction semantics mechanically correspond to the modernized versions of the SECD machine and to the best of our knowledge, they provide the first syntactic theories of applicative expressions with the J operator

How we might be able to Understand the Brain

Current methodologies in the neurosciences have difficulty in accounting for complex phenomena such as language, which can however be quite well characterised in phenomenological terms. This paper addresses the issue of unifying the two approaches. We typically understand complicated systems in terms of a collection of models, each characterisable in principle within a formal system, it being possible to explain higher-level properties in terms of lower level ones by means of a series of inferences based on these models. We consider the nervous system to be a mechanism for implementing the demands of an appropriate collection of models, each concerned with some aspect of brain and behaviour, the observer mechanism of Baas playing an important role in matching model and behaviour in this context. The discussion expounds these ideas in detail, showing their potential utility in connection with real problems of brain and behaviour, important areas where the ideas can be applied including the development of higher levels of abstraction, and linguistic behaviour, as described in the works of Karmiloff-Smith and Jackendoff respectively

Extra argumentality - affectees, landmarks, and voice

This article investigates sentences with additional core arguments of a special type in three languages, viz. German, English, and Mandarin. These additional arguments, called extra arguments in the article, form a crosslinguistically homogeneous class by virtue of their structural and semantic similarities, with so-called "raised possessors" forming just a sub-group among them. Structurally, extra arguments may not be the most deeply embedded arguments in a sentence. Semantically, their referents are felt to stand in a specific relation to the referent of the/a more deeply embedded argument. There are two major thematic relations that are instantiated by extra arguments, viz. affectees and landmarks. These thematic role notions are justified in the context of and partly in contrast to, Dowty's (1991) proto-role approach. An affectee combines proto-agent with proto-patient properties in eventualities that are construed as involving causation. A landmark is a ground with respect to some spatial configuration denoted by the predication at hand, but a figure at the highest level of gestalt partitioning that is relevant in a clause. Thereby, both affectees and landmarks are inherently hybrid categories. The account of extra argumentality is couched in a neo-Davidsonian event semantics in the spirit of Kratzer (1996, 2003), and voice heads are assumed to introduce affectee arguments and landmark arguments right above VP

Deduction over Mixed-Level Logic Representations for Text Passage Retrieval

A system is described that uses a mixed-level representation of (part of) meaning of natural language documents (based on standard Horn Clause Logic) and a variable-depth search strategy that distinguishes between the different levels of abstraction in the knowledge representation to locate specific passages in the documents. Mixed-level representations as well as variable-depth search strategies are applicable in fields outside that of NLP.Comment: 8 pages, Proceedings of the Eighth International Conference on Tools with Artificial Intelligence (TAI'96), Los Alamitos C

On the axiomatic systems of syntactically-categorial languages

The paper contains an overview of the most important results presented in the monograph of the author "Teorie Językow Syntaktycznie-Kategorialnych" ("Theories of Syntactically-Categorial Languages" (in Polish), PWN, Warszawa-Wrocław 1985. In the monograph four axiomatic systems of syntactically-categorial languages are presented. The first two refer to languages of expression-tokens. The others also takes into consideration languages of expression-types. Generally, syntactically-categorial languages are languages built in accordance with principles of the theory of syntactic categories introduced by S. Leśniewski [1929,1930]; they are connected with- the Ajdukiewicz’s work [1935] which was a continuation of Leśniewski’s idea and further developed and popularized in the research on categorial grammars, by Y. Bar-Hillel [1950,1953,1964]. To assign a suitable syntactic category to each word of the vocabulary is the main idea of syntactically-categorial approach to language. Compound expressions are built from the words of the vocabulary and then a suitable syntactic-category is assigned to each of them. A language built in this way should be decidable, which means that there should exist an algorithm for deciding about each expression of it, whether it is well-formed or is syntactically connected . The traditional, originating from Husserl, understanding of the syntactic category confronts some difficulties. This notion is defined by abstraction using the concept of affiliation of two expressions to the same syntactic category

Trustworthy Refactoring via Decomposition and Schemes: A Complex Case Study

Widely used complex code refactoring tools lack a solid reasoning about the correctness of the transformations they implement, whilst interest in proven correct refactoring is ever increasing as only formal verification can provide true confidence in applying tool-automated refactoring to industrial-scale code. By using our strategic rewriting based refactoring specification language, we present the decomposition of a complex transformation into smaller steps that can be expressed as instances of refactoring schemes, then we demonstrate the semi-automatic formal verification of the components based on a theoretical understanding of the semantics of the programming language. The extensible and verifiable refactoring definitions can be executed in our interpreter built on top of a static analyser framework.Comment: In Proceedings VPT 2017, arXiv:1708.0688