82 research outputs found
A Poly-Connexive Logic
The paper introduces a variant of connexive logic in which connexivity is extended from the interaction of negation with implication to the interaction of negation also with conjunction and disjunction. The logic is presented by two deductively equivalent methods: an axiomatic one and a natural-deduction one. Both are shown to be complete for a four-valued model theory
Phrasal Coordination Relatedness Logic
I presented a sub-classical relating logic based on a relating via an NL-inspired relating relation Rcss. The relation Rcss is motivated by the NL-phenomenon of phrasal (subsentential) coordination, exhibiting an important aspect of contents relating among the arguments of binary connectives. The resulting logic Lcss can be viewed as a relevance logic exhibiting a contents related relevance, stronger than the variable-sharing property of other relevance logics like R. Note that relating here is not “tailored” to justify some predetermined logic; rather, the relating relation is independently justified, and induces a logic not previously investigated
Relevant Connexive Logic
In this paper, a connexive extension of the Relevance logic R→ was presented. It is defined by means of a natural deduction system, and a deductively equivalent axiomatic system is presented too. The goal of such an extension is to produce a logic with stronger connection between the antecedent and the consequent of an implication
Does the Implication Elimination Rule Need a Minor Premise?
The paper introduces NJ g , a variant of Gentzen’s NJ natural deduction system, in which the implication elimination rule has no minor premise. The NJ g -systems extends traditional ND-system with a new kind of action in derivations, assumption incorporation, a kind of dual to the assumption discharge action. As a result, the implication (I/E)-rules are invertible and, almost by definition, harmonious and stable, a major condition imposed by proof-theoretic semantics on ND-systems to qualify as meaning-conferring. There is also a proof-term assignment to NJ g -derivations, materialising the Curry-Howard correspondence for this system
Amalia -- A Unified Platform for Parsing and Generation
Contemporary linguistic theories (in particular, HPSG) are declarative in
nature: they specify constraints on permissible structures, not how such
structures are to be computed. Grammars designed under such theories are,
therefore, suitable for both parsing and generation. However, practical
implementations of such theories don't usually support bidirectional processing
of grammars. We present a grammar development system that includes a compiler
of grammars (for parsing and generation) to abstract machine instructions, and
an interpreter for the abstract machine language. The generation compiler
inverts input grammars (designed for parsing) to a form more suitable for
generation. The compiled grammars are then executed by the interpreter using
one control strategy, regardless of whether the grammar is the original or the
inverted version. We thus obtain a unified, efficient platform for developing
reversible grammars.Comment: 8 pages postscrip
Parsing with Typed Feature Structures
In this paper we provide for parsing with respect to grammars expressed in a
general TFS-based formalism, a restriction of ALE. Our motivation being the
design of an abstract (WAM-like) machine for the formalism, we consider parsing
as a computational process and use it as an operational semantics to guide the
design of the control structures for the abstract machine.
We emphasize the notion of abstract typed feature structures (AFSs) that
encode the essential information of TFSs and define unification over AFSs
rather than over TFSs. We then introduce an explicit construct of multi-rooted
feature structures (MRSs) that naturally extend TFSs and use them to represent
phrasal signs as well as grammar rules. We also employ abstractions of MRSs and
give the mathematical foundations needed for manipulating them. We then present
a simple bottom-up chart parser as a model for computation: grammars written in
the TFS-based formalism are executed by the parser. Finally, we show that the
parser is correct.Comment: PostScript, 15 pages; Proc. 4th Intl. Workshop on Parsing
Technologies, Prague, September 199
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