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This is a comment on a translation of Franz von Kutschera's paper ‘Ein verallgemeinerter Widerlegungsbegriff für Gentzenkalküle’, which was published in German in 1969. The paper is an important predecessor of what is nowadays called ‘proof-theoretic semantics’, which describes the view that the meaning of logical connectives is determined by the rules governing their use in a proof system. Von Kutschera adopts this view in this paper, and more specifically, a bilateralist view on this subject in that his aim is to give a general framework that provides generalized rule schemata for arbitrary connectives both for proving and refuting and to use this as a reference to prove completeness of certain systems of operators purely proof-theoretically. The main logical system in focus here has been shown to be equivalent to N4, Nelson's constructive logic with strong negation. In order to understand the translated paper better, a contextualizing comment is offered referring and relating it to a preceding paper by von Kutschera. [ABSTRACT FROM AUTHOR]

Rumfitt has given two arguments that in unilateralist verificationist theories of meaning, truth collapses into correct assertibility. In the present paper I give similar arguments that show that in unilateral falsificationist theories of meaning, falsehood collapses into correct deniability. According to bilateralism, meanings are determined by assertion and denial conditions, so the question arises whether it succumbs to similar arguments. I show that this is not the case. The final section considers the question whether a principle central to Rumfitt's first argument, 'It is assertible that A if and only if it is assertible that it is assertible that A', is one that bilateralists can reject, and concludes that they cannot. It follows that the logic of assertibility and deniability, according to a result by Williamson, is the little known modal logic K4 studied by Sobociński. The paper ends with a plaidoyer for bilateralists to adopt this logic. [ABSTRACT FROM AUTHOR]

In a recent paper del Valle-Inclan and Schloder argue that bilateral calculi call for their own notion of proof-theoretic harmony, distinct from the usual (or 'unilateral') ones. They then put forward a specifically bilateral criterion of harmony, and present a harmonious bilateral calculus for classical logic. In this paper, I show how del Valle-Inclan and Schlöder's criterion of harmony suggests a notion of normal form for bilateral systems, and prove normalisation for two (harmonious) bilateral calculi for classical logic, HB1 and HB2. The resulting normal derivations have the usual desirable features, like the separation and subformula properties. HB1-normal form turns out to be strictly stronger that the notion of normal form proposed by Nils Kurbis, and HB2-normal form is neither stronger nor weaker than a similar proposal by Marcello D'Agostino, Dov Gabbay, and Sanjay Modgyl. [ABSTRACT FROM AUTHOR]

Proof-theoretic semantics (P-tS) is the paradigm of semantics in which meaning in logic is based on proof (as opposed to truth). A particular instance of P-tS for intuitionistic propositional logic (IPL) is its base-extension semantics (B-eS). This semantics is given by a relation called support, explaining the meaning of the logical constants, which is parameterized by systems of rules called bases that provide the semantics of atomic propositions. In this paper, we interpret bases as collections of definite formulae and use the operational view of them as provided by uniform proof-search|the proof-theoretic foundation of logic programming (LP)|to establish the completeness of IPL for the B-eS. This perspective allows negation, a subtle issue in P-tS, to be understood in terms of the negation-as-failure protocol in LP. Specifically, while the denial of a proposition is traditionally understood as the assertion of its negation, in B-eS we may understand the denial of a proposition as the failure to find a proof of it. In this way, assertion and denial are both prime concepts in P-tS. [ABSTRACT FROM AUTHOR]

Natural deduction with alternatives extends Gentzen-Prawitz-style natural deduction with a single structural addition: negatively signed assumptions, called alternatives. It is a mildly bilateralist, single-conclusion natural deduction proof system in which the connective rules are unmodified from the usual Prawitz introduction and elimination rules|the extension is purely structural. This framework is general: it can be used for (1) classical logic, (2) relevant logic without distribution, (3) affine logic, and (4) linear logic, keeping the connective rules fixed, and varying purely structural rules. The key result of this paper is that the two principles that introduce kinds of irrelevance to natural deduction proofs: (a) the rule of explosion (from a contradiction, anything follows); and (b) the structural rule of vacuous discharge; are shown to be two sides of a single coin, in the same way that they correspond to the structural rule of weakening in the sequent calculus. The paper also includes a discussion of assumption classes, and how they can play a role in treating additive connectives in substructural natural deduction. [ABSTRACT FROM AUTHOR]

Pak--Saudi relations are exclusive, cordial, and strategic. The elementary features of this exceptional relationship are strong religious affinity, bilateral resolve, assured support, and pragmatism. This resilient and all-weather relationship started much before the Kingdom became oil-rich. Since the beginning of the 1950s, Pak-Saudi relations have been witnessing an upward trajectory in all diplomatic fields, including political, economic, social, and strategic cooperation. While attaining dynamism in their bilateral relationship, both countries urge more exclusivity, steadiness, and perpetuity in their relations as reinforcing factors. The role of national institutions of both countries has been commendable in evolving and consolidating their traditional bondage. This paper, therefore, underlines the need that despite changes in the regional and global geopolitical situations, both countries must extend unwavering support to each other on the issues of their national interests, regional security, and sustainable development. [ABSTRACT FROM AUTHOR]

Proof-theoretic semantics is an inferentialist theory of meaning originally developed in a unilateral framework. Its extension to bilateral systems opens both opportunities and problems. The problems are caused especially by Coordination Principles (a kind of rule that is not present in unilateral systems) and mismatches between rules for assertion and rules for rejection. In this paper, a solution is proposed for two major issues: the availability of a reduction procedure for tonk and the existence of harmonious rules for the paradoxical zero-ary connective •. The solution is based on a reinterpretation of bilateral rules as com-plex rules, that is, rules that introduce or eliminate connectives in a subordinate position. Looking at bilateral rules from this perspective, the problems faced by bilateralism can be seen as special cases of general problems of complex systems, which have been already analyzed in the literature. In the end, a comparison with other proposed solutions underlines the need for further investigation in order to complete the picture of bilateral proof-theoretic semantics. [ABSTRACT FROM AUTHOR]

In order to counter China’s rising influence, US is finding more allies in South Asia. As a result, it has been signing various agreements with India to strengthen its footsteps in the region. Due to the mutual interests and shared values of both the partners, they have come close to each other through the civil nuclear cooperation. This is causing a number of concerns for the neighbors as US-India partnership is proving highly beneficial for both of the states at the international arena. India is becoming a source of balancing power for the US to retain its influence in the Pacific and Indian oceans against the rising power, China and its allies. Contrary to this, India is also getting benefit from US in terms of strengthening its military capabilities using the state-of-the-art technologies provided by the US, posing many security implications for the adversaries and neighbors of India. India-US strategic partnership is causing a shift in balance of power in India’s favor which can be dangerous for Pakistan’s security. In this scenario, Pakistan can never afford to remain oblivious of the developments taking place between these two countries because of its security concerns. These developments can undermine Pakistan’s deterrent capabilities and can weaken its position in the Indo-Pak strife over the Kashmir issue. Consequently, Pakistan will have to work with China to strengthen its bond to counter the negative effects caused by the USIndia partnership. Also, it will have to rethink its foreign policy towards the eastern countries and will have to establish cordial bilateral relations with its neighbors. This paper covers all the aspects of bilateral partnership between India and the USA and its implications for Pakistan economically, politically, strategically and diplomatically. This research aims to analyze the emerging strategic partnership between the United States and India and its implications for Pakistan. Moreover, a descriptive-analytical method has been adopted to carry out this research work. [ABSTRACT FROM AUTHOR]

Copyright of Análisis Filosófico is the property of Sociedad Argentina de Analisis Filosofico and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

The categoricity problem for a system of logic reveals an asymmetry between the model-theoretic and the proof-theoretic resources of that logic. In particular, it reveals prima facie that the proof-theoretic instruments are insufficient for matching the envisaged model-theory, when the latter is already available. Among the proposed solutions for solving this problem, some make use of new proof-theoretic instruments, some others introduce new model-theoretic constrains on the proof-systems, while others try to use instruments from both sides. On the proof-theoretical side, two main approaches for solving the categoricity problem for propositional classical logic consist in the enforcement of the formal systems of this logic by introducing rules of inference of a new kind. A multiple-conclusions logic allows rules of inference with more than one conclusion, while a bilateralist system contains rules of inference formulated in terms of assertion and rejection. Both these approaches reveal interesting formal features of logical reasoning. This paper analyses some of the advantages and limitations of these two approaches as solutions for a full formalization of logic, i.e., for a categorical formalization [ABSTRACT FROM AUTHOR]

Pak–Saudi relations are exclusive, cordial, and strategic. The elementary features of this exceptional relationship are strong religious affinity, bilateral resolve, assured support, and pragmatism. This resilient and all-weather relationship started much before the Kingdom became oil-rich. Since the beginning of the 1950s, Pak-Saudi relations have been witnessing an upward trajectory in all diplomatic fields, including political, economic, social, and strategic cooperation. While attaining dynamism in their bilateral relationship, both countries urge more exclusivity, steadiness, and perpetuity in their relations as reinforcing factors. The role of national institutions of both countries has been commendable in evolving and consolidating their traditional bondage. This paper, therefore, underlines the need that despite changes in the regional and global geopolitical situations, both countries must extend unwavering support to each other on the issues of their national interests, regional security, and sustainable development. Bibliography Entry Khan, Muhammad, and Sidra Khan. 2021. "Evolving Nature of Pak-Saudi Relationship." Margalla Papers 25 (1): 59-69.

Filinski and Griffin have independently succeeded in extending the formulae-as-types notion to deal with continuations. Whereas Griffin adopted control operators primitively, Filinski adopted the duality of functions to construct a symmetric lambda-calculus in which continuations are first-class objects. In this paper, we construct a typed lambda-calculus with first-class configurations consisting of expressions and continuations of the same types. Our calculus corresponds to a natural deduction based on Rumfitt's bilateralism. Function types are represented as the implication and but-not connectives in intuitionistic and paraconsistent logics, respectively. Our calculus is not only logically consistent, but also computationally consistent. Our calculus with call-by-value and call-by-name strategies correspond to Wadler's call-by-value and call-by-name dual calculi, respectively. Furthermore, we propose a notion of relaxed configurations, which loosely take expressions and continuations of different types. We confirm that the relaxedness defines control operators for delimited continuations. [ABSTRACT FROM AUTHOR]

In a recent paper del Valle-Inclan and Schlöder argue that bilateral calculi call for their own notion of proof-theoretic harmony, distinct from the usual (or ‘unilateral’) ones. They then put forward a specifically bilateral criterion of harmony, and present a harmonious bilateral calculus for classical logic. In this paper, I show how del Valle-Inclan and Schlöder’s criterion of harmony suggests a notion of normal form for bilateral systems, and prove normalisation for two (harmonious) bilateral calculi for classical logic, HB1 and HB2. The resulting normal derivations have the usual desirable features, like the separation and subformula properties. HB1-normal form turns out to be strictly stronger that the notion of normal form proposed by Nils Kürbis, and HB2-normal form is neither stronger nor weaker than a similar proposal by Marcello D’Agostino, Dov Gabbay, and Sanjay Modgyl.

Copyright of Ermeni Arastirmalari is the property of Center for Eurasian Studies and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

This paper is dedicated to developing a formalism that takes rejection seriously. Bilateral notation of signed formulas with force indicators is adopted to define signed consequences which can be viewed as the bilateral counterpart of Tarskian consequence relations. Its relation to some other bilateral approaches is discussed. It is shown how David Nelson's logic N4 can be characterized bilaterally and the corresponding completeness result is proved. Further, bilateral variants of three familiar notions are considered and investigated: that of a fragment, of definitional equivalence, and of a conservative extension. [ABSTRACT FROM AUTHOR]

The standard notion of formal theory, in logic, is in general biased exclusively towards assertion: it commonly refers only to collections of assertions that any agent who accepts the generating axioms of the theory should also be committed to accept. In reviewing the main abstract approaches to the study of logical consequence, we point out why this notion of theory is unsatisfactory at multiple levels, and introduce a novel notion of theory that attacks the shortcomings of the received notion by allowing one to take both assertions and denials on a par. This novel notion of theory is based on a bilateralist approach to consequence operators, which we hereby introduce, and whose main properties we investigate in the present paper. [ABSTRACT FROM AUTHOR]

Natural deduction with alternatives extends Gentzen–Prawitz-style natural deduction with a single structural addition: negatively signed assumptions, called alternatives. It is a mildly bilateralist, single-conclusion natural deduction proof system in which the connective rules are unmodi_ed from the usual Prawitz introduction and elimination rules — the extension is purely structural. This framework is general: it can be used for (1) classical logic, (2) relevant logic without distribution, (3) affine logic, and (4) linear logic, keeping the connective rules fixed, and varying purely structural rules. The key result of this paper is that the two principles that introduce kinds of irrelevance to natural deduction proofs: (a) the rule of explosion (from a contradiction, anything follows); and (b) the structural rule of vacuous discharge; are shown to be two sides of a single coin, in the same way that they correspond to the structural rule of weakening in the sequent calculus. The paper also includes a discussion of assumption classes, and how they can play a role in treating additive connectives in substructural natural deduction.

Inferentialism is a theory in the philosophy of language which claims that the meanings of expressions are constituted by inferential roles or relations. Instead of a traditional model-theoretic semantics, it naturally lends itself to a proof-theoretic semantics, where meaning is understood in terms of inference rules with a proof system. Most work in proof-theoretic semantics has focused on logical constants, with comparatively little work on the semantics of non-logical vocabulary. Drawing on Robert Brandom's notion of material inference and Greg Restall's bilateralist interpretation of the multiple conclusion sequent calculus, I present a proof-theoretic semantics for atomic sentences and their constituent names and predicates. The resulting system has several interesting features: (1) the rules are harmonious and stable; (2) the rules create a structure analogous to familiar model-theoretic semantics; and (3) the semantics is compositional, in that the rules for atomic sentences are determined by those for their constituent names and predicates. [ABSTRACT FROM AUTHOR]

There are many ways of understanding what it is for an argument to be valid. Although we usually identify the concept of validity with (classical first-order) logical validity and, in turn, we typically take this to capture the notion of necessary preservation of truth in virtue of logical form, this is just one way in which validity can be explained. A different understanding of the notion of validity that has received some attention recently is based on the idea that an argument is valid just in case accepting its premises is incoherent with rejecting its conclusion. The main claim of the paper will be that, under this understanding of the notion of validity, the usual reasons to privilege a treatment of validities over a treatment of invalidities loose much of their force. Validity and invalidity are on a par, which means that there are no strong reasons to treat validities primitively and to define invalidities in terms of them. [ABSTRACT FROM AUTHOR]

Purpose – The multilateral liberalisation of trade in education under the General Agreement on Trade in Services (GATS) has achieved little progress. In a bid to overcome this lacklustre education trade liberalisation under the World Trade Organization (WTO), the purpose of this paper is to examine education trade bilateralism between Australia and India as an alternative to multilateralism. The end is to maximise bilateral trade liberalisation in education as a means to facilitate dynamic productivity gains, export opportunities, market competition, and FDI in the sector. The combined effect of this bilateralism would help accelerate economic growth in both countries, which is likely to generate domino effects on other WTO members, thereby contributing to the multilateral liberalisation of trade in services under the WTO. Design/methodology/approach – The research methodology is analytical, based on pertinent empirical and secondary information. Findings – Strong complementarities and synergies are found for the integration of trade in education services between Australia and India. Of the major exporters of education services, Australia enjoys the most competitive edge and comparative advantage in the Asia-Pacific. India faces strong demands for quality education services due to its economic reforms and expansion requiring knowledge-based workforce for high efficiency and productivity and has become a major importer of education services in the region. Originality/value – The paper identifies new means of consolidating Australia and India's existing trade, niche areas of further opportunities, and potential challenges to be confronted for greater economic integration through trade in education. The originality of the paper lies in its core message that education trade bilateralism can be a valuable stepping stone, in many instances, to multilateral trade in education. [ABSTRACT FROM AUTHOR]

On a bilateralist reading, sequents are interpreted as statements to the effect that, given the assertion of the antecedent it is incoherent to deny the succedent. This interpretation goes against its own ecumenical ambitions, endowing Cut with a meaning very close to that of tertium non datur and thus rendering it intuitionistically unpalatable. This paper explores a top-down route for arguing that, even intuitionistically, a prohibition to deny is as strong as a licence to assert. [ABSTRACT FROM AUTHOR]

The Central Asian republics (CARs), which emerged as independent states in the post-Soviet phase, faced several challenges. During the Soviet era, the CARs were agriculturally oriented towards the Soviet economy and, accordingly, river water management was also centralized under the command economic model. However, with the collapse of the Soviet Union, the CARs had to review the existing water management arrangements. This is where the absence of a Moscow-centric central authority has proven detrimental to the region endowed with two major rivers and their several subsidiaries. In this context, the paper suggests an emphasis on multilateralism, rather than bilateralism, as a more feasible approach to river water management. Clearly, multilateralism would promote a more equitable solution compared to bilateralism, which does not adopt a holistic approach to the region. Considering the fact that the region is characterized by a water crisis in addition to the fragility of the environment makes a multilateral arrangement significantly more appropriate for the region in the long term. [ABSTRACT FROM AUTHOR]

This paper examines the evolution of the dairy complexes of New Zealand and Chile in the context of increasing bilateral interaction between the two countries, and their recent signing of a ‘Trans-Pacific Strategic Economic Partnership’ (TPSEP) free-trade agreement. The two economies can be said to occupy semi-peripheral positions in global markets and have, through the twentieth and into the twenty-first century, increasingly competed for market share in a range of primary product (particularly agricultural)-based export markets. Similar sets of historical processes, although variably timed, have shaped the roles of New Zealand and Chile respectively as resource peripheries, and the extent to which the two countries can collaborate for mutual benefit and transcend these roles is uncertain. In taking a sectoral approach this paper questions the compatibility of the two dairy complexes in the context of the TPSEP, and recommends further sectoral and localised studies in order to better appraise the model of ‘co-opetition’ promoted through the agreement. [ABSTRACT FROM AUTHOR]