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

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

Another plan for negation

The paper  presents a plan for negation, proposing a paradigm shift from the Australian plan for negation,  leading to a family of contra-classical logics. The two main ideas are the following:  Instead of shifting points of evaluation (in a frame), shift the evaluated formula. Introduce an incompatibility set for every atomic formula, extended to any compound formula, and impose the condition on valuations that a formula evaluates to true iff all the formulas in its incompatibility set evaluate to false. Thus, atomic sentences are not independent in their truth-values.  The resulting negation, in addition to excluding the negated formula, provides a positive alternative to the negated formula. I  also present a sound and complete natural deduction proof systems for those logics. In addition, the kind of negation considered in this paper is shown to provide an innovative notion of grounding negation.  &nbsp