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Abstract. We propose intersection type assignment systems for two resource control term calculi: the lambda calculus and the sequent lambda calculus with explicit operators for weakening and contraction. These resource control calculi, λ and λ Gtz , respectively, capture the computational content of intuitionistic natural deduction and intuitionistic sequent logic with explicit structural rules. Our main contribution is the characterisation of strong normalisation of reductions in both calculi. We first prove that typability implies strong normalisation in λ by adapting the reducibility method. Then we prove that typability implies strong normalisation in λ Gtz by using a combination of well-orders and a suitable embedding of λ Gtz -terms into λ -terms which preserves types and enables the simulation of all its reductions by the operational semantics of the λ -calculus. Finally, we prove that strong normalisation implies typability in both systems using head subject expansion.

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This paper gives a characterisation, via intersection types, of the strongly normalising proof-terms of an intuitionistic sequent calculus (where LJ easily embeds). The soundness of the typing system is reduced to that of a well known typing system with intersection types for the ordinary λ-calculus. The completeness of the typing system is obtained from subject expansion at root position. Next we use our result to analyze the characterisation of strong normalisability for three classes of intuitionistic terms: ordinary λ-terms, ΛJ-terms (λ-terms with generalised application), and λx-terms (λ-terms with explicit substitution). We explain via our system why the type systems in the natural deduction format for ΛJ and λx known from the literature contain extra, exceptional rules for typing generalised application or substitution; and we show a new characterisation of the β-strongly normalising λ-terms, as a corollary to a PSN-result, relating the λ-calculus and the intuitionistic sequent calculus. Finally, we obtain variants of our characterisation by restricting the set of assignable types to sub-classes of intersection types, notably strict types. In addition, the known characterisation of the β-strongly normalising λ-terms in terms of assignment of strict types follows as an easy corollary of our results.

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PurposeThis study aims to illuminate the relationship between the logistic performance indexes (LPIs) of trade countries and sharing obligations related to logistics services in delivery among parties in international sales contracts.Design/methodology/approachA comprehensive one-year database of Serbian international trade flows is used. The LPIs of 148 countries are related to the Incoterms® rules in international sales contracts that designate the division of obligations between exporters and importers for moving goods. Empirical data were subjected to statistical analysis, where nonparametric correlation and inferential methods were applied. The differences between countries with the highest and lowest LPIs were also examined.FindingsLPIs positively correlate with logistics commitments in exports and imports. Their impact on the choice of Incoterms® rules differs among the groups of trade terms. Waterway and D-terms are the most sensitive. LPIs of trade countries clearly impact “emission” and “attraction” of the most extended sellers' delivery obligation “packages,” expressed in D rules.Research limitations/implicationsThe empirical data are limited to a single country. Further research must explore the relative impact of macrologistic factors on exporters and importers' logistics commitments for building better decision-making support tools.Practical implicationsThe results may support suppliers and buyers in sharing their experiences on Incoterms® practice and encourage more rational than intuitive decisions.Originality/valueThis is the first empirical study to quantitatively evidence the sensitivity of groups of Incoterms® rules on the macrologistic environment of trade countries.

International supply chains generate substantial amounts of CO2 emissions. However, established methodologies for national freight transport emission assessments do not consider such international perspectives sufficiently. This research aims to show how logistic responsibility may be used in ex post transport CO2 emission assessments, for macrologistic or supply chain levels. We propose an original approach to estimate and allocate CO2 emissions generated by international freight transport between trade countries. The proposed method relies on the applied Incoterms® rules in sales contracts. A new indicator, the index of responsibility for transport emissions (RTE-index), is introduced to allocate bilateral trade-related transport CO2 emissions. This is the first time that the Incoterms® clauses are used for macrologistic assessments of international trade-related transport CO2 emissions. Our approach is exemplified using bilateral trade-related transport flows between Serbia and other European countries. The introduced RTE-index is expected to help visualise average national trade-related transport CO2 emission responsibilities; increase awareness regarding environmental considerations among trade parties, logistics companies, and national organisations; and provide new perspectives for environmental transport policy actions.