Analyticity,Balance and Non-admissibility of $$\varvec{Cut}$$ Cut in Stoic Logic

Studia Logica - This paper shows that, for the Hertz–Gentzen Systems of 1933 (without Thinning), extended by a classical rule T1 (from the Stoics) and using certain axioms (also from the...     

Proof-Theoretic Semantics for Subsentential Phrases

The paper briefly surveys the sentential proof-theoretic semantics for fragment of English. Then, appealing to a version of Frege’s context-principle (specified to fit type-logical grammar), a method is presented for deriving proof-theoretic meanings for sub-sentential phrases, down to lexical units (words). The sentential meaning is decomposed according to the function-argument structure as determined by the type-logical grammar. In doing so, the paper presents a novel proof-theoretic interpretation of simple type, replacing Montague’s model-theoretic type interpretation (in arbitrary Henkin models). The domains of derivations are collections of derivations in the associated “dedicated” natural-deduction proof-system, and functions therein (with no appeal to models, truth-values and elements of a domain). The compositionality of the semantics is analyzed.     

Distance‐Based Measures of Specialization and Balance in Multi‐Criteria: A DEA‐Integrated Method

Decision makers pursuing several distinct goals may differ in their behaviour. Some try to achieve all goals simultaneously, whereas others concentrate on only certain ones and are therefore specialized. We present a new method of measuring the specialization degree with respect to a given standard balanced relation of the goals. The measurement is integrated into data envelopment analysis (DEA) methodology, uses a non‐compensative distance measure, permits optional convex polyhedral cones as predefined balance sets and guarantees feasible solutions. Geometrically, it is based on the angle between the balance cone and the ray through the point of investigation. The proposed models can be used to support and complement the usual effectiveness and efficiency analysis in multi‐criteria decision analysis and DEA. They are motivated and illustrated by a simple numerical example, compared with an alternative method recently published and applied to real data from the literature. Copyright © 2014 John Wiley & Sons, Ltd.     

A Note on Harmony

In the proof-theoretic semantics approach to meaning, harmony, requiring a balance between introduction-rules (I-rules) and elimination rules (E-rules) within a meaning conferring natural-deduction proof-system, is a central notion. In this paper, we consider two notions of harmony that were proposed in the literature: 1. GE-harmony, requiring a certain form of the E-rules, given the form of the I-rules. 2. Local intrinsic harmony: imposes the existence of certain transformations of derivations, known as reduction and expansion. We propose a construction of the E-rules (in GE-form) from given I-rules, and prove that the constructed rules satisfy also local intrinsic harmony. The construction is based on a classification of I-rules, and constitute an implementation to Gentzen’s (and Pawitz’) remark, that E-rules can be “read off” I-rules.     

Cut-Elimination and a Permutation-Free Sequent Calculus for Intuitionistic Logic

We describe a sequent calculus, based on work of Herbelin, of which the cut-free derivations are in 1-1 correspondence with the normal natural deduction proofs of intuitionistic logic. We present a simple proof of Herbelin's strong cut-elimination theorem for the calculus, using the recursive path ordering theorem of Dershowitz.