The article presents proofs of the context freeness of a family of typelogical grammars, namely all grammars that are based on a uni- ormultimodal logic of pure residuation, possibly enriched with thestructural rules of Permutation and Expansion for binary modes.

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 (...) class='Hi'>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. (shrink)

Consider a general class of structural inference rules such as exchange, weakening, contraction and their generalizations. Among them, some are harmless but others do harm to cut elimination. Hence it is natural to ask under which condition cut elimination is preserved when a set of structural rules is added to a structure-free logic. The aim of this work is to give such a condition by using algebraic semantics. We consider full Lambek calculus (FL), i.e., intuitionistic logic (...) without any structural rules, as our basic framework. Residuated lattices are the algebraic structures corresponding to FL. In this setting, we introduce a criterion, called the propagation property, that can be stated both in syntactic and algebraic terminologies. We then show that, for any set R of structural rules, the cut elimination theorem holds for FL enriched with R if and only if R satisfies the propagation property. As an application, we show that any set R of structural rules can be "completed" into another set R*, so that the cut elimination theorem holds for FL enriched with R*, while the provability remains the same. (shrink)

We study structural rules in the context of multi-valued logics with finitely-many truth-values. We first extend Gentzen’s traditional structural rules to a multi-valued logic context; in addition, we propos some novel structural rules, fitting only multi-valued logics. Then, we propose a novel definition, namely, structural rules completeness of a collection of structural rules, requiring derivability of the restriction of consequence to atomic formulas by structural rules only. The restriction (...) to atomic formulas relieves the need to concern logical rules in the derivation. (shrink)

The article presents proofs of the context freeness of a family of typelogical grammars, namely all grammars that are based on a uni- ormultimodal logic of pure residuation, possibly enriched with thestructural rules of Permutation and Expansion for binary modes.

Atocha Aliseda’s Abductive Reasoning (2006) gives a structural characterization of the “forward” explana-tory reasoning from a theory to observational data. This paper asks whether there are any interesting structural rules for the “backward” abductive reasoning from observations to explanatory theories. Ignoring statistical cases, a partial explication of abduction is converse deductive explanation: h is abducible from e iff h deductively explains e. This relation of abducibility trivially satisfies Converse Entailment (if h entails e, then h is abducible (...) from e ), but it does not generally satisfy Converse Consequence (if h is abducible from e and g entails h, then g is abducible from e ), since deductive explanation is not always transitive. (shrink)

In recent years, substructural approaches to paradoxes have become quite popular. But whatever restrictions on structural rules we may want to enforce, it is highly desirable that such restrictions be accompanied by independent philosophical motivation, not directly related to paradoxes. Indeed, while these recent developments have shed new light on a number of issues pertaining to paradoxes, it seems that we now have even more open questions than before, in particular two very pressing ones: what (independent) motivations do (...) we have (if any) for restrictions on structural rules, and what to make of the plurality of new logics emerging from these restrictions, i.e. how to ‘choose’ among the different options. In this paper, we address these two questions from the perspective of a dialogical conception of logic that we've been advocating in recent years. We will argue that dialogical interpretations of structural rules, that is, as rules determining specific properties of the dialogues in question, provide a conveniently neutral framework to adjudicate between the different substructural proposals that have been made in the literature on paradoxes. (shrink)

In our previous paper [5], we have studied Kripke-type semantics for propositional logics without the contraction rule. In this paper, we will extend our argument to predicate logics without the structure rules. Similarly to the propositional case, we can not carry out Henkin's construction in the predicate case. Besides, there exists a difficulty that the rules of inference () and () are not always valid in our semantics. So, we have to introduce a notion of normal models.

Different natural deduction proof systems for intuitionistic and classical logic —and related logical systems—differ in fundamental properties while sharing significant family resemblances. These differences become quite stark when it comes to the structural rules of contraction and weakening. In this paper, I show how Gentzen and Jaśkowski’s natural deduction systems differ in fine structure. I also motivate directed proof nets as another natural deduction system which shares some of the design features of Genzen and Jaśkowski’s systems, but which (...) differs again in its treatment of the structural rules, and has a range of virtues absent from traditional natural deduction systems. (shrink)

We show that if the structural rules are admissible over a set \ of atomic rules, then they are admissible in the sequent calculus obtained by adding the rules in \ to the multisuccedent minimal and intuitionistic \ calculi as well as to the classical one. Two applications to pure logic and to the sequent calculus with equality are presented.

According to semantic antirealism, intuitionistic logic satisfies the requirement that truth should be constrained by provability in principle. Some philosophers have argued that semantic antirealism must be committed to effective provability and that the commitment leads to a stronger kind of logical revisionism exemplified by substructural logics. I shall take into account two different kinds of reply. The first is concerned with meaning per se and grasp or fixing of meaning. It rests on the idea that if we have a (...) method which may be used over some surveyable range, we have determined a way of applying the method everywhere in principle, and that this is enough as far as fixing or grasping meaning is concerned. The second concerns two radical antirealist principles disqualifying structural rules: Token Preservation and Preservation of Local Feasibility. Against criticisms, I shall argue that conceptual support may be provided for both. The main point in this debate is that there is a decisive difference between the rejection of classical logic via the curbing of the epistemic idealizations embedded in structural rules and the rejection of classical logic via the intuitionistic criticism of invalid introduction and elimination rules. It will be explained why the second rejection is stronger than the former. (shrink)

The contraction-free sequent calculus G4 for intuitionistic logic is extended by rules following a general rule-scheme for nonlogical axioms. Admissibility of structural rules for these extensions is proved in a direct way by induction on derivations. This method permits the representation of various applied logics as complete, contraction- and cut-free sequent calculus systems with some restrictions on the nature of the derivations. As specific examples, intuitionistic theories of apartness and order are treated.

The goal of the paper is to develop a universal semantic approach to derivable rules of propositional multiple-conclusion sequent calculi with structural rules, which explicitly involve not only atomic formulas, treated as metavariables for formulas, but also formula set variables, upon the basis of the conception of model introduced in :27–37, 2001). One of the main results of the paper is that any regular sequent calculus with structural rules has such class of sequent models that (...) a rule is derivable in the calculus iff it is sound with respect to each model of the semantics. We then show how semantics of admissible rules of such calculi can be found with using a method of free models. Next, our universal approach is applied to sequent calculi for many-valued logics with equality determinant. Finally, we exemplify this application by studying sequent calculi for some of such logics. (shrink)

We give a direct proof of admissibility of cut and contraction for the contraction-free sequent calculus G4ip for intuitionistic propositional logic and for a corresponding multi-succedent calculus: this proof extends easily in the presence of quantifiers, in contrast to other, indirect, proofs. i.e., those which use induction on sequent weight or appeal to admissibility of rules in other calculi.

We give a direct proof of admissibility of cut and contraction for the contraction-free sequent calculus G4ip for intuitionistic propositional logic and for a corresponding multi-succedent calculus: this proof extends easily in the presence of quantifiers, in contrast to other, indirect, proofs. i.e., those which use induction on sequent weight or appeal to admissibility of rules in other calculi.

Written with verve and intensity (and a good bit of wordplay), this is the long-awaited study of Flaubert and the modern literary field that constitutes the ...

The logical formalism of abductive reasoning is still an open discussion and various theories have been presented about it. Abduction is a type of non-monotonic and defeasible reasonings, and the logic containing such a reasoning is one of the types of non-nonmonotonic and defeasible logics, such as inductive logic. Abduction is a kind of natural reasoning and it is a solution to the problems having this form "the phenomenon of φ cannot be explained by the theory of Θ" and we (...) need to search for (or to adduce) an explanation for φ. Taking α as the explanation and <Θ,φ> as the abductive problem, Θ∪{α}⊨φ is the logical format of a strong abductive reasoning. In this article, the proof theory for first-order abductive calculus is proposed based on Gentzen-type first-order proof theory. Considering its dual, i.e., the semantic tableaux, and without the need to translate the formulas, this calculation is sound and complete. After examining the structural rules of this calculus, some metalogical considerations and open problems such as consistency, completeness and undecidability of this account have been addressed. (shrink)

This paper shows a role of the contraction rule in decision problems for the logics weaker than the intuitionistic logic that are obtained by deleting some or all of structural rules. It is well-known that for such a predicate logic L, if L does not have the contraction rule then it is decidable. In this paper, it will be shown first that the predicate logic FLec with the contraction and exchange rules, but without the weakening rule, is (...) undecidable while the propositional fragment of FLec is decidable. On the other hand, it will be remarked that logics without the contraction rule are still decidable, if our language contains function symbols. (shrink)

Gentzen’s classical sequent calculus has explicit structural rules for contraction and weakening. They can be absorbed by replacing the axiom P,¬P by Γ,P,¬P for any context Γ, and replacing the original disjunction rule with Γ,A,B implies Γ,AB.This paper presents a classical sequent calculus which is also free of contraction and weakening, but more symmetrically: both contraction and weakening are absorbed into conjunction, leaving the axiom rule intact. It uses a blended conjunction rule, combining the standard context-sharing and context-splitting (...) rules: Γ,Δ,A and Γ,Σ,B implies Γ,Δ,Σ,AB. We refer to this system as minimal sequent calculus.We prove a minimality theorem for the propositional fragment : any propositional sequent calculus S is complete if and only if S contains. Thus one can view as a minimal complete core of Gentzen’s. (shrink)

In this paper, we propose a game semantics for the (associative) Lambek calculus . Compared to the implicational fragment of intuitionistic propositional calculus, the semantics deals with two features of the logic: absence of structural rules, as well as directionality of implication. We investigate the impact of these variations of the logic on its game semantics.

As far as logic is concerned, the conclusion of Michael Dummett's manifestability argument is that intuitionistic logic, as first developed by Heyting, satisfies the semantic requirements of antirealism. The argument may be roughly sketched as follows: since we cannot manifest a grasp of possibly justification-transcendent truth conditions, we must countenance conditions which are such that, at least in principle and by the very nature of the case, we are able to recognize that they are satisfied whenever they are. Intuitionistic logic (...) satisfies the semantic requirement that we should either eschew the notion of truth altogether and replace it by provability in principle, or constrain it by provability in principle (Dummett [1973] 1978). (Handout: 1-5). Some philosophers have argued that the traditional antirealist desideratum of decidability in principle is too weak, so that semantic antirealism properly construed must be committed to effective decidability. As such, it either leads to strict finitism (Wright [1982] 1993) [Handout: 6] or to a much stronger kind of logical revisionism than the one considered by intuitionists (whether or not they accept the manifestability argument): substructural logics, and in particular linear logics, rather than intuitionistic logic, satisfy the semantic requirements of strict antirealism (Dubucs and Marion 2004) [Handout: 8-9]. I shall develop two different kinds of replies. The first is concerned with the notion of meaning per se and looks to strict finitism directly, although not on the ground that it would provide a correct way of dealing with Soritic-type paradoxes (the original and primary focus of discussion in Wright [1982] 1993). The second is concerned with the justification of structural and logical rules in a natural deduction system à la Gentzen. It will deal in particular with the criticism of the structural rules of Weakening and Contraction [Handout: 10 and 11]. The first kind of reply, which Dummett has partially taken into consideration, is that if we jettison the effectively vs. in principle distinction, as applied to manifestability-type arguments, we end up with an unsatisfactory explanation of how the meaning of statements covering the practically unsurveyable or pro tempora undecided cases is fixed. The idea is that if we have a method which may be used over some small range, we have determined a way of applying the method everywhere in principle and that this is enough as far as fixing meaning is concerned. Decidability in principle is just what we need with respect to manifestation of grasp of meaning. In this perspective, antirealism shouldn't be strict and manifestability-type arguments need not be applied as far as the strict finitist would want to [Handout: 7]. It follows that there is no reason to think that practical feasibility should be built in assertibility conditions and proofs be construed dynamically as acts in the strict antirealist's acception of that term [Handout: 8]. I shall then look at one radical antirealist principle disqualifying structural rules, namely Token Preservation, arguing against Bonnay and Cozic's criticisms of Dubucs and Marion (Bonnay and Cozic 3 2007) that some conceptual support may be provided for Token Preservation, which doesn't rely on a causal misreading of the turnstile [Handout: 13, 14]. I shall then assess the merits and limits of radical antirealism and the logic of feasible proofs with respect to the original Dummettian argument in favour of semantic antirealism (provided it has indeed revisionist implications for logic), whether the radical antirealist merely stipulates what human feasibility amounts to, or dispenses with structural rules in order to argue in favour of a curb on the epistemic idealizations they unwarrantedly embed. It will be noted here that there is a great difference, conceptually speaking, between the rejection of classical logic via the curbing of the epistemic idealizations embedded in structural rules, and the rejection of classical logic via the criticism of the introduction and elimination rules which fix the meaning of the classical constants. The kind of logical revisionism envisaged by intuitionists from Heyting on is in many respects stronger than the one envisaged by advocates of linear logic, should they ground their arguments on an endorsement of strict antirealism. The crucial case of excluded middle is telling. Because of the splitting of the constants in linear logic (Handout: 12], two distinct laws of excluded middle may be formulated (Handout: 15), but the traditional arguments of Brouwer and Heyting against the classical law yield a stronger revision than the substructural revision with its admission of these two (very) weak versions of the law. (Project: a clearer conception is needed of how the introduction and elimination rules for the logical connectives in the intuitionistic calculus depend on the structural rules which the radical antirealist wishes to reject.). (shrink)

Some empirical evidence in the artificial language acquisition literature has been taken to suggest that statistical learning mechanisms are insufficient for extracting structural information from an artificial language. According to the more than one mechanism (MOM) hypothesis, at least two mechanisms are required in order to acquire language from speech: (a) a statistical mechanism for speech segmentation; and (b) an additional rule-following mechanism in order to induce grammatical regularities. In this article, we present a set of neural network studies (...) demonstrating that a single statistical mechanism can mimic the apparent discovery of structural regularities, beyond the segmentation of speech. We argue that our results undermine one argument for the MOM hypothesis. (shrink)

This provocative book outlines a powerful and original theory of liberty structured by the liberal conception of justice and the rule of law. Drawing on insights from philosophy, political theory, economics, and law, he shows how this new conception of liberty can confront, and solve, the central societal problems of knowledge, interest, and power.

In Rules and Representations, first published in 1980, Noam Chomsky lays out many of the concepts that have made his approach to linguistics and human cognition so instrumental to our understanding of language.Chomsky arrives at his well-known position that there is a universal grammar, structured in the human mind and common to all human languages. Based on Chomsky's 1978 Woodbridge Lectures, this edition contains revised versions of the lectures and two new essays.

The idea that correspondences relating grammatical relations and semantics (argument structure constructions) are needed to account for simple sentence types is reviewed, clarified, updated and compared with two lexicalist alternatives. Traditional lexical rules take one verb as ‘input’ and create (or relate) a different verb as ‘output’. More recently, invisible derivational verb templates have been proposed, which treat argument structure patterns as zero derivational affixes that combine with a root verb to yield a new verb. While the derivational template (...) perspective can address several problems that arise for traditional lexical rules, it still faces problems in accounting for idioms, which often contain specifications that are not appropriately assigned to individual verbs or derivational affixes (regarding adjuncts, modification, and inflection). At the same time, it is clear that verbs play a central role in determining their distribution. The balance between verbs and phrasal argument structure constructions is addressed via the Principles of Semantic Coherence and Correspondence together with a usage-based hierarchy of constructions that contains entries which can include particular verbs and other lexical material. (shrink)

The idea that correspondences relating grammatical relations and semantics (argument structure constructions) are needed to account for simple sentence types is reviewed, clarified, updated and compared with two lexicalist alternatives. Traditional lexical rules take one verb as ‘input’ and create (or relate) a different verb as ‘output’. More recently, invisible derivational verb templates have been proposed, which treat argument structure patterns as zero derivational affixes that combine with a root verb to yield a new verb. While the derivational template (...) perspective can address several problems that arise for traditional lexical rules, it still faces problems in accounting for idioms, which often contain specifications that are not appropriately assigned to individual verbs or derivational affixes (regarding adjuncts, modification, and inflection). At the same time, it is clear that verbs play a central role in determining their distribution. The balance between verbs and phrasal argument structure constructions is addressed via the Principles of Semantic Coherence and Correspondence together with a usage‐based hierarchy of constructions that contains entries which can include particular verbs and other lexical material. (shrink)

In this provocative and engaging new book, Randy Barnett outlines a powerful and original theory of liberty structured by the liberal conception of justice and the rule of law. Drawing on insights from philosophy, political theory, economics, and law, he shows how this new conception of liberty can confront, and solve, the central societal problems of knowledge, interest, and power.

Understanding whether the long and elaborate songs of male gibbons have syntax and hierarchical structures is an interesting question in the evolution of language, because gibbons are near humans in the phylogenetic tree and a hierarchically organized syntax is considered to be a basic component of human language. We conducted field research at Danum Valley Conservation Area in northern Borneo to test the hypothesis that gibbon songs have syntax and chunks. We followed one Mueller’s gibbon group for 1 week in (...) the dry and rainy seasons every year from 2001 to 2009, collecting vocal and behavioral data. Results show that songs emitted by the studied male gibbon were governed by combinatory rules. Some context-dependent songs had different combinatory rules, although they overlapped with the songs whose contexts were uncertain. The male Mueller’s songs had characteristics that suggest existence of chunk structure. These results provided an important perspective in the study of language origin. (shrink)

Rosenkranz (2021) offered a logic and a detailed account of justification, according to which justification that p can be analyzed as a form of second-level ignorance: ¬K¬Kp. An intuition behind the analysis is that the justified subject has the potential, at least in a nearby world, to either come to know p or come to know ¬Kp. However, given Rosenkranz’s hyperintensional semantics for modeling knowledge states, we can always construct, out of an ¬K¬K-agent’s knowledge state, epistemic possibilities that prohibit the (...) agent from having that potential. This shows that Rosenkranz’s analysis is still insufficient for carrying all the epistemic weight underlying the notion of justification. A better analysis would require a deeper look into an agent’s knowledge structure and its involved modalities, which could be a lot more complex than what the ¬K¬K rule tells us. (shrink)

A NewsFusion System is a logic-based system for merging heterogeneous structured news reports. Structured news reports are XML documents, where the textentries are restricted to individual words or simple phrases, such as names and domain-specific terminology, and numbers and units. We assume structured news reports do not require natural language processing. In previous papers, we have presented aspects of a logic-based framework for merging structured news reports based on fusion rules. Fusion rules are a form of scripting language (...) that define how structured news reports should be merged. The antecedent of a fusion rule is a call to investigate the information in the structured news reports and the background knowledge, and the consequent of a fusion rule is a formula specifying an action to be undertaken to form a merged report. It is expected that a set of fusion rules is defined for any given application. In this paper, we present a framework for aggregation predicates that can be used in fusion rules for context-dependent aggregation of structured news reports. We also present a case study that uses aggregation predicates to merge weather reports that have been obtained from a selection of websites. (shrink)

This paper provides a formal description of two legal domains. In addition, we describe the generation of various artificial datasets from these domains and explain the use of these datasets in previous experiments aligning learning and reasoning. These resources are made available for the further investigation of connections between arguments, cases and rules. The datasets are publicly available at https://github.com/CorSteging/LegalResources.

This essay enriches causal models capturing the propagation of prejudice, bias, and other aggregative social mechanisms, negative or positive. These explananda include the reinforcement of economic inequality, “mob-like” behavior, peer pressure, and the establishment of social norms. The stage is set by introducing various forms of redundant causation and discussing some difficulties with mainstream preemption. Next the main proposal extends current representations of aggregative social mechanisms in two respects. First, it is more nuanced, as it identifies three distinct kinds of (...) inferences: relevance of causes to effects, degree of redundancy of an effect, and the influence that causes exert on other causes. Second, it offers a quantitative—as opposed to merely qualitative—distinction between the causal contribution of preempting and preempted causes. (shrink)

The ways in which the sciences have been delineated and categorized throughout history provide insights into the formation, stabilization, and establishment of scientific systems of knowledge. The Dresdener school’s approach for explaining and categorizing the genesis of the engineering disciplines is still valid, but needs to be complemented by further-reaching methodological and theoretical reflections. Pierre Bourdieu’s theory of social practice is applied to the question of how individual agents succeed in influencing decisively a discipline’s changing object orientation, institutionalisation and self-reproduction. (...) Through the accumulation of social, cultural and economic capital, they succeed in realising their own organisational ideas and scientific programs. Key concepts for the analysis include the struggle for power and resources, monopolies of interpretation, and the degree of autonomy. A case study from the Aachener Technische Hochschule shows that the consolidation of ferrous metallurgy can be conceived as a symbolical struggle between Fritz Wüst, professor for ferrous metallurgy, and the German Iron and Steel Institute, leading to a construction of a system of differences in which scientists accepted being scientists rather than entrepreneurs, and entrepreneurs accepted becoming entrepreneurs and renounced science. (shrink)

: For the purposes of interpretation and constructive engagement, the structure and content of Confucius' version of the Golden Rule (CGR) is examined by elaborating its three dimensions as suggested in the Analects. It is argued that the CGR, which consists of two intertwined central ideas in Confucius' ethics, shu and zhong, involves three interdependent and complementary dimensions: (1) the methodological (i.e., the methodological aspect of shu), which consists of the principles of reversibility and extensibility; (2) the internal starting point (...) (i.e., the substantial aspect of shu), which somehow points to the fundamental virtue ren and constitutes the internal starting point for applying the methodological principles of the CGR; and (3) the external starting point (i.e., zhong as one's sincere and devoted commitment to those established social constituents specified by the li, regardless of the involved moral recipient's social status), which constitutes the external starting point for applying the methodological principles of the CGR. (shrink)

Severe acute respiratory syndrome‐coronavirus (SARS‐CoV)‐2′s origin is still controversial. Genomic analyses show SARS‐CoV‐2 likely to be chimeric, most of its sequence closest to bat CoV RaTG13, whereas its receptor binding domain (RBD) is almost identical to that of a pangolin CoV. Chimeric viruses can arise via natural recombination or human intervention. The furin cleavage site in the spike protein of SARS‐CoV‐2 confers to the virus the ability to cross species and tissue barriers, but was previously unseen in other SARS‐like CoVs. (...) Might genetic manipulations have been performed in order to evaluate pangolins as possible intermediate hosts for bat‐derived CoVs that were originally unable to bind to human receptors? Both cleavage site and specific RBD could result from site‐directed mutagenesis, a procedure that does not leave a trace. Considering the devastating impact of SARS‐CoV‐2 and importance of preventing future pandemics, researchers have a responsibility to carry out a thorough analysis of all possible SARS‐CoV‐2 origins. (shrink)

This provocative book outlines a powerful and original theory of liberty structured by the liberal conception of justice and the rule of law. Drawing on insights from philosophy, political theory, economics, and law, he shows how this new conception of liberty can confront, and solve, the central societal problems of knowledge, interest, and power.

A theory of analogy must describe how the meaning of an analogy is derived from the meanings of its parts. In the structure‐mapping theory, the interpretation rules are characterized as implicit rules for mapping knowledge about a base domain into a target domain. Two important features of the theory are (a) the rules depend only on syntactic properties of the knowledge representation, and not on the specific content of the domains; and (b) the theoretical framework allows analogies (...) to be distinguished cleanly from literal similarity statements, applications of abstractions, and other kinds of comparisons.Two mapping principles are described: (a) Relations between objects, rather than attributes of objects, are mapped from base to target; and (b) The particular relations mapped are determined by systematicity, as defined by the existence of higher‐order relations. (shrink)