In this paper we carry out an algebraic investigation of the weak nilpotent minimum logic and its t-norm based axiomatic extensions. We consider the algebraic counterpart of WNM, the variety of WNM-algebras and prove that it is locally finite, so all its subvarieties are generated by finite chains. We give criteria to compare varieties generated by finite families of WNM-chains, in particular varieties generated by standard WNM-chains, or equivalently t-norm based axiomatic extensions of WNM, and (...) we study their standard completeness properties. We also characterize the generic WNM-chains, i. e. those that generate the variety [MATHEMATICAL DOUBLE-STRUCK CAPITAL W]ℕ[MATHEMATICAL DOUBLE-STRUCK CAPITAL M], and we give finite axiomatizations for some t-norm based extensions of WNM. (shrink)

Monoidal triangular norm logic MTL is the logic of left-continuous triangular norms. In the paper we present a relational formalization of the logic MTL and then we introduce relational dual tableau that can be used for verification of validity of MTL-formulas. We prove soundness and completeness of the system.

For each continuous t-norm &, a class of fuzzy topological spaces, called &-topological spaces, is introduced. The motivation stems from the idea that to each many-valued logic there may correspond a theory of many-valued topology, in particular, each continuous t-norm may lead to a theory of fuzzy topology. It is shown that for each continuous t-norm &, the subcategory consisting of &-topological spaces is simultaneously reflective and coreflective in the category of fuzzy topological spaces, hence gives (...) rise to an autonomous theory of fuzzy topology. Topologizing a fuzzy pre-ordered set with the fuzzy Scott topology yields a functor from the category of fuzzy pre-ordered sets and maps that preserve suprema of flat ideals to the category of &-topological spaces. It is proved that this functor is a full one if and only if the t-norm & is Archimedean. (shrink)

In many-valued logics with the unit interval as the set of truth values, from the standard negation and the product (or, more generally, from any strict Frank t-norm) all measurable logical functions can be derived, provided that also operations with countable arity are allowed. The question remained open whether there are other t-norms with this property or whether all strict t-norms possess this property. We give a full solution to this problem (in the case of strict t-norms), together with (...) convenient sufficient conditions. We list several families of strict t-norms having this property and provide also counterexamples (the Hamacher product is one of them). Finally, we discuss the consequences of these results for the characterization of tribes based on strict t-norms. (shrink)

The monoidal t-norm based logic MTL is obtained from Hájek''s Basic Fuzzy logic BL by dropping the divisibility condition for the strong (or monoidal) conjunction. Recently, Jenei and Montgana have shown MTL to be standard complete, i.e. complete with respect to the class of residuated lattices in the real unit interval [0,1] defined by left-continuous t-norms and their residua. Its corresponding algebraic semantics is given by pre-linear residuated lattices. In this paper we address the (...) issue of standard and rational completeness (rational completeness meaning completeness with respect to a class of algebras in the rational unit interval [0,1]) of some important axiomatic extensions of MTL corresponding to well-known parallel extensions of BL. Moreover, we investigate varieties of MTL algebras whose linearly ordered countable algebras embed into algebras whose lattice reduct is the real and/or the rational interval [0,1]. These embedding properties are used to investigate finite strong standard and/or rational completeness of the corresponding logics. (shrink)

The monoidal t-norm based logic MTL is obtained from Hájek's Basic Fuzzy logic BL by dropping the divisibility condition for the strong (or monoidal) conjunction. Recently, Jenei and Montgana have shown MTL to be standard complete, i.e. complete with respect to the class of residuated lattices in the real unit interval [0,1] defined by left-continuous t-norms and their residua. Its corresponding algebraic semantics is given by pre-linear residuated lattices. In this paper we address the (...) issue of standard and rational completeness (rational completeness meaning completeness with respect to a class of algebras in the rational unit interval [0,1]) of some important axiomatic extensions of MTL corresponding to well-known parallel extensions of BL. Moreover, we investigate varieties of MTL algebras whose linearly ordered countable algebras embed into algebras whose lattice reduct is the real and/or the rational interval [0,1]. These embedding properties are used to investigate finite strong standard and/or rational completeness of the corresponding logics. (shrink)

In general, there is only one fuzzy logic in which the standard interpretation of the strong conjunction is a strict triangular norm, namely, the product logic. We study several equations which are satisfied by some strict t-norms and their dual t-conorms. Adding an involutive negation, these equations allow us to generate countably many logics based on strict t-norms which are different from the product logic.

Monoidal t-norm based logic $\mathbf {MTL}$ is the weakest t-norm based residuated fuzzy logic, which is a $[0,1]$ -valued propositional logical system having a t-norm and its residuum as truth function for conjunction and implication. Monadic fuzzy predicate logic $\mathbf {mMTL\forall }$ that consists of the formulas with unary predicates and just one object variable, is the monadic fragment of fuzzy predicate logic $\mathbf {MTL\forall }$, which is indeed the predicate (...) version of monoidal t-norm based logic $\mathbf {MTL}$. The main aim of this paper is to give an algebraic proof of the completeness theorem for monadic fuzzy predicate logic $\mathbf {mMTL\forall }$ and some of its axiomatic extensions. Firstly, we survey the axiomatic system of monadic algebras for t-norm based residuated fuzzy logic and amend some of them, thus showing that the relationships for these monadic algebras completely inherit those for corresponding algebras. Subsequently, using the equivalence between monadic fuzzy predicate logic $\mathbf {mMTL\forall }$ and S5-like fuzzy modal logic $\mathbf {S5(MTL)}$, we prove that the variety of monadic MTL-algebras is actually the equivalent algebraic semantics of the logic $\mathbf {mMTL\forall }$, giving an algebraic proof of the completeness theorem for this logic via functional monadic MTL-algebras. Finally, we further obtain the completeness theorem of some axiomatic extensions for the logic $\mathbf {mMTL\forall }$, and thus give a major application, namely, proving the strong completeness theorem for monadic fuzzy predicate logic based on involutive monoidal t-norm logic $\mathbf {mIMTL\forall }$ via functional representation of finitely subdirectly irreducible monadic IMTL-algebras. (shrink)

Axiomatizations are presented for fuzzy logics characterized by uninorms continuous on the half-open real unit interval [0,1), generalizing the continuous t-norm based approach of Hájek. Basic uninorm logic BUL is defined and completeness is established with respect to algebras with lattice reduct [0,1] whose monoid operations are uninorms continuous on [0,1). Several extensions of BUL are also introduced. In particular, Cross ratio logic CRL, is shown to be complete with respect to one special uninorm. A Gentzen-style (...) hypersequent calculus is provided for CRL and used to establish co-NP completeness results for these logics. (shrink)

The rearrangement inequality states that the sum of products of permutations of 2 sequences of real numbers are maximized when the terms are similarly ordered and minimized when the terms are ordered in opposite order. We show that similar inequalities exist in algebras of multi-valued logic when the multiplication and addition operations are replaced with various T-norms and T-conorms respectively. For instance, we show that the rearrangement inequality holds when the T-norms and T-conorms are derived from Archimedean copulas.

The last decade has seen an enormous development in infinite-valued systems and in particular in such systems which have become known as mathematical fuzzy logics. The paper discusses the mathematical background for the interest in such systems of mathematical fuzzy logics, as well as the most important ones of them. It concentrates on the propositional cases, and mentions the first-order systems more superficially. The main ideas, however, become clear already in this restricted setting.

In this paper we prove strong completeness of axiomatic extensions of first-order strict core fuzzy logics with the so-called quasi-witnessed axioms with respect to quasi-witnessed models. As a consequence we obtain strong completeness of Product Predicate Logic with respect to quasi-witnessed models, already proven by M.C. Laskowski and S. Malekpour in [19]. Finally we study similar problems for expansions with Δ, define Δ-quasi-witnessed axioms and prove that any axiomatic extension of a first-order strict core fuzzy logic, expanded with (...) Δ, and Δ-quasi-witnessed axioms are complete with respect to Δ-quasi-witnessed models. (shrink)

ABSTRACT A new algebraic construction -called rotation- is introduced in this paper which from any left-continuous triangular norm which has no zero divisors produces a left-continuous but not continuous triangular norm with strong induced negation. An infinite number of new families of such triangular norms can be constructed in this way which provides a huge spectrum of choice for e.g. logical and set theoretical connectives in non-classical logic and in fuzzy theory. On the other (...) hand, the introduced construction brings us closer to the understanding the structure of these connectives and the corresponding logics. From the application point of view, results of this paper can be especially useful in the field of non-classical logic, fuzzy sets, and fuzzy preference modeling. (shrink)

This paper aims at being a systematic investigation of different completeness properties of first-order predicate logics with truth-constants based on a large class of left-continuous t-norms . We consider standard semantics over the real unit interval but also we explore alternative semantics based on the rational unit interval and on finite chains. We prove that expansions with truth-constants are conservative and we study their real, rational and finite chain completeness properties. Particularly interesting is the case of considering canonical (...) real and rational semantics provided by the algebras where the truth-constants are interpreted as the numbers they actually name. Finally, we study completeness properties restricted to evaluated formulae of the kind , where φ has no additional truth-constants. (shrink)

This paper is the continuation of [11] where the rotation construction of left-continuous triangular norms was presented. Here the class of triangular subnorms and a second construction, called rotation-annihilation, are introduced: Let T1 be a left-continuous triangular norm. If T1 has no zero divisors then let T2 be a left-continuous rotation invariant t-subnorm. If T1 has zero divisors then let T2 be a left-continuous rotation invariant triangular norm. From each such pair the rotation-annihilation construction (...) produces a left-continuous triangular norm with strong induced negation. An infinite number of new families of such triangular norms can be constructed in this way, and this further extends our spectrum of choice for the proper triangular norm e.g. in probabilistic metric spaces, or for logical and set theoretical connectives in non-classical logic, or e.g. in fuzzy sets theory and its applications. On the other hand, the introduced construction brings us closer to the understanding of the structure of these operations. (shrink)

This paper is a contribution to Mathematical fuzzy logic, in particular to the algebraic study of t-norm based fuzzy logics. In the general framework of propositional core and Δ-core fuzzy logics we consider three properties of completeness with respect to any semantics of linearly ordered algebras. Useful algebraic characterizations of these completeness properties are obtained and their relations are studied. Moreover, we concentrate on five kinds of distinguished semantics for these logics–namely the class of algebras defined over (...) the real unit interval, the rational unit interval, the hyperreals , the strict hyperreals and finite chains, respectively–and we survey the known completeness methods and results for prominent logics. We also obtain new interesting relations between the real, rational and hyperreal semantics, and good characterizations for the completeness with respect to the semantics of finite chains. Finally, all completeness properties and distinguished semantics are also considered for the first-order versions of the logics where a number of new results are proved. (shrink)

Abstract.ΠMTL is a schematic extension of the monoidal t-norm based logic (MTL) by the characteristic axioms of product logic. In this paper we prove that ΠMTL satisfies the standard completeness theorem. From the algebraic point of view, we show that the class of ΠMTL-algebras (bounded commutative cancellative residuated l-monoids) in the real unit interval [0,1] generates the variety of all ΠMTL-algebras.

Logical pluralism is the view that there is more than one correct logic. A key objection to logical pluralism is that it collapses into monism. The core of the Collapse Objection is that only the pluralist’s strongest logic does any genuine normative work; since a logic must do genuine normative work, this means that the pluralist is really a monist, who is committed to her strongest logic being the one true logic. This paper considers a (...) neglected question in the collapse debate: what is it for a logic to do genuine normative work? As well as having wider upshot for the connection between logic and normativity, grappling with this question provides a new response to the Collapse Objection on behalf of the pluralist. I suggest that we should allow logics to generate pro tanto reasons in a way that bears not just on combinations of attitudes but on how an agent’s attitudes are based on one another. This motivates adopting normative principles that allow the pluralist’s weaker logics to earn their normative keep. Rather than being ad hoc, these principles capture a sense in which good reasoning goes beyond the consistency of an agent’s attitudes. Good reasoning is also concerned with how an agent’s attitudes are based on one another. (shrink)

It is shown that given any finite system of monoid identities, it is decidable if the class of locally finite monoids that satisfy the system is a variety. This answers an open problem of Mark V. Sapir.

In this paper I construct a system of semantics for classical and intuitionistic propositional logic based on epistemic norms governing belief expansion. Working in the AGM-framework of belief change, I give a generalisation of Gärdenfors’ notion of belief systems which can be defined without reference to a logical consequence operator by using a version of the Ramsey Test. These belief expansion systems can then be used to define epistemic models which are sound and complete for either classical or (...) intuitionistic propositional logic depending on which of the two notions of epistemic validity, identified by Levi and Arló-Costa, is used. Finally, I offer a discussion on how these results can be understood as providing a model theory within the framework of logical expressivism. (shrink)

We study the forcing operators on MTL-algebras, an algebraic notion inspired by the Kripke semantics of the monoidal t -norm based logic . At logical level, they provide the notion of the forcing value of an MTL-formula. We characterize the forcing operators in terms of some MTL-algebras morphisms. From this result we derive the equality of the forcing value and the truth value of an MTL-formula.

Normative arrow update logic (NAUL) is a logic that combines normative temporal logic (NTL) and arrow update logic (AUL). In NAUL, norms are interpreted as arrow updates on labeled transition systems with a CTL-like logic. We show that the satisfiability problem of NAUL is decidable with a tableau method and it is in EXPSPACE.

Each Girard quantale (i.e., commutative quantale with a selected dualizing element) provides a support for a semantics for linear propositional formulas (but not for linear derivations). Several constructions of Girard quantales are known. We give two more constructions, one using an arbitrary partially ordered monoid and one using a partially ordered group (both commutative). In both cases the semantics can be controlled be a relation between pairs of elements of the support and formulas. This gives us a neat way of (...) handling duality. (shrink)

Each Girard quantale (i.e., commutative quantale with a selected dualizing element) provides a support for a semantics for linear propositional formulas (but not for linear derivations). Several constructions of Girard quantales are known. We give two more constructions, one using an arbitrary partially ordered monoid and one using a partially ordered group (both commutative). In both cases the semantics can be controlled be a relation between pairs of elements of the support and formulas. This gives us a neat way of (...) handling duality. (shrink)

Each Girard quantale provides a support for a semantics for linear propositional formulas. Several constructions of Girard quantales are known. We give two more constructions, one using an arbitrary partially ordered monoid and one using a partially ordered group. In both cases the semantics can be controlled be a relation between pairs of elements of the support and formulas. This gives us a neat way of handling duality.

Deontic logic is devoted to the study of logical properties of normative predicates such as permission, obligation and prohibition. Since it is usual to apply these predicates to actions, many deontic logicians have proposed formalisms where actions and action combinators are present. Some standard action combinators are action conjunction, choice between actions and not doing a given action. These combinators resemble boolean operators, and therefore the theory of boolean algebra offers a well-known athematical framework to study the properties of (...) the classic deontic operators when applied to actions. In his seminal work, Segerberg uses constructions coming from boolean algebras to formalize the usual deontic notions. Segerberg’s work provided the initial step to understand logical properties of deontic operators when they are applied to actions. In the last years, other authors have proposed related logics. In this chapter we introduce Segerberg’s work, study related formalisms and investigate further challenges in this area. (shrink)

What really makes the concepts of obligation or permission so important for practical philosophy? What if we could find a better concept, one that, despite the simplicity, could show itself as intuitive and rich as possible? Could justifications be used in common language and practice as a sign of ethical judgment and as a strong motive for action? In most scenarios, for example, it really doesn’t matter if a given action is obliged, permitted or forbidden, one may perform the action (...) as long as a justification for doing it is present. In this sense, the notion of justification seems to be more basic and powerful than other concepts used in the philosophical discourse. The existence of formal systems based on the epistemological side of justification, created by Artemov, led us primarily to think that justification could make the formal discourse much more accurate for ethics than the ones using deontological concepts. In the semantical and syntactical aspects, almost all of Artemov’s systems directly proved to be fruitful for ethical purposes. We also developed combinations between the standard deontic logic and logics of justification, resulting in what whe called the Logics of Normative Justification. These systems were able to change the object of the justification formulas and shed some light in ethics as a whole, normative and metaethics. Metaethics were a forgotten subject in formal ethics. We were also able to deal with some known problems in deontic logic, like the famous Ross’s paradox and the expressiveness of prima facie and all-things-considered obligations. (shrink)

Physical laws are irresistible. Logical rules are not. That is why logic is said to be normative. Given a system of logic we have a Norma, a standard of correctness. The problem is that we need another Norma to establish when the standard of correctness is to be applied. Subsequently we start by clarifying the senses in which the term ‘Iogic’ and the term ‘normativity’ are being used. Then we explore two different epistemologies for logic to see (...) the sort of defence of the normativity of logic they allow for; if any. The analysis concentrates on the case of classical logic. In particular the issue will be appraised from the perspective put forward by the epistemology based on the methodology of wide reflective equilibrium and the scientific one underlying the view of logic as model. (shrink)

In this article, we present an argumentative approach to normative reasoning. Special attention is paid to deontic conflicts, contrary-to-duty and specificity cases, which are modelled by means of argumentative attacks. For this, we adopt a recently proposed framework for logical argumentation in which arguments are generated by a sequent calculus of a given base logic of Argument & Computation ), and use standard deontic logic as our base logic. Argumentative attacks are realized by elimination rules that allow (...) to discharge specific sequents. We demonstrate the usefulness of our approach by means of various well-known benchmark examples, and show that this approach is rich enough to capture a variety of paradigms for handling conflicting norms such as reasoning with maximally consistent sets, prioritized norms and deontic formalisms based on I/O logic. (shrink)

This work has been selected by scholars as being culturally important and is part of the knowledge base of civilization as we know it. This work is in the public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity has a copyright on the body of the work. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and (...) made generally available to the public. To ensure a quality reading experience, this work has been proofread and republished using a format that seamlessly blends the original graphical elements with text in an easy-to-read typeface. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant. (shrink)

In this thesis, I develop and investigate various novel semantic frameworks for deontic logic. Deontic logic concerns the logical aspects of normative reasoning. In particular, it concerns reasoning about what is required, allowed and forbidden. I focus on two main issues: free-choice reasoning and the role of norms in deontic logic. -/- Free-choice reasoning concerns permissions and obligations that offer choices between different actions. Such permissions and obligations are typically expressed by a disjunctive clause in the scope (...) of a deontic operator. For instance, the sentence "Jane may take an apple or a pear" intuitively offers Jane a choice between two permitted courses of action: she may take an apple, and she may take a pear. In the first part of the thesis, I develop semantic frameworks for deontic logic that account for free-choice reasoning. I show that the resulting logics avoid problems that arise for other logical accounts of free-choice reasoning. The main technical contributions are completeness results for axiomatizations of the different logics. -/- Semantic frameworks for deontic logic typically only talk about norms implicitly. In the second part of the thesis, I clarify the role of norms in deontic logic. I develop a formal model of normative systems where norms are represented explicitly. The model takes into account both the hierarchical structure of normative systems, and the function of norms to regulate agent behavior. I show how the model can be used to clarify issues in the study of normative systems. I also develop a norm-based semantics for deontic action logic based on the model. (shrink)

In this chapter, we will first argue that current practices in CBE are framed within the market or economic logic and miss the normative dimension of the call for circularity. The transition to the CBE requires a fundamental reflection on the role of economic actors in the social and ecological environment with significant consequences for their business practices. Second, we will argue that the transition to the CBE requires the acknowledgement of the normative and social dimensions of this transition (...) at the meso and macro levels, and the establishment of an environmental and social logic on the micro level of business practices. Third, we will argue that the concept of responsible innovation (RI) can help to articulate the normative and social dimensions of the transition to the CBE, and enables the operationalisation of the environmental and social logic at the micro level. In this respect, RI can be understood as a driver for the transition to the CBE. (shrink)

Physical laws are irresistible. Logical rules are not. That is why logic is said to be normative. Given a system of logic we have a Norma, a standard of correctness. The problem is that we need another Norma to establish when the standard of correctness is to be applied. Subsequently we start by clarifying the senses in which the term "logic" and the term "normativity" are being used. Then we explore two different epistemologies for logic to (...) see the sort of defence of the normativity of logic they allow for; if any. The analysis concentrates on the case of classical logic. In particular the issue will be appraised from the perspective put forward by the epistemology based on the methodology of wide reflective equilibrium and the scientific one underlying the view of logic as model. (shrink)

This book presents adaptive logics as an intuitive and powerful framework for modeling defeasible reasoning. It examines various contexts in which defeasible reasoning is useful and offers a compact introduction into adaptive logics. The author first familiarizes readers with defeasible reasoning, the adaptive logics framework, combinations of adaptive logics, and a range of useful meta-theoretic properties. He then offers a systematic study of adaptive logics based on various applications. The book presents formal models for defeasible reasoning stemming from different (...) contexts, such as default reasoning, argumentation, and normative reasoning. It highlights various meta-theoretic advantages of adaptive logics over other logics or logical frameworks that model defeasible reasoning. In this way the book substantiates the status of adaptive logics as a generic formal framework for defeasible reasoning. (shrink)

The paper deals with the problem of the nature of logic and its normativity in the context of the normativity of scientific knowledge in general. We proceed from a division between fundamental aspects of scientific knowledge which are related to the nature and subject matter of particular sciences, and its applied aspects which are related to the possible applications of sciences. This division fully applies to logic. The authors note that if we view logic as a completely (...) objective discipline, devoid of any "anthropological basis", then the only rational alternative to anti-realist approaches is an ontological (realistic) strategy to justify the logical ones that seek to justify a certain kind of being. To do this, it is necessary to abandon the normative interpretation of logical evaluations and logical systems. Logic can gain a true ontological foundation, based on the devoid of the normative color of understanding logical evaluations as a particular kind of object. Logic has both a deductive core, and various applied disciplines, modern informal logic among them. While formal deductive logic is concentrated on the systems of abstract logical entities (objects) such as truth values and logical functions, the main task of informal logic consist in studying a real argument, which people apply in communicative processes, by elaborating certain standards, criteria and procedures for their interpretation and evaluation. No science can be normative in its basic (fundamental) aspects, and so is logic. Nevertheless, any science is in some degree normative with respect to its applied aspects, and informal logic perfectly illustrates this in view of a normative evolving of applied systems of the modern theories of argumentation. In addition to denying the normativity of formal deductive logic as a fundamental theoretical discipline, the authors of this article demonstrate the fundamental possibility of normative measurement of logical knowledge, in particular in the applied aspect of the development of modern informal logic. (shrink)

This paper proposes an approach to investigate norm-governed learning agents which combines a logic-based formalism with an equation-based counterpart. This dual formalism enables us to describe the reasoning of such agents and their interactions using argumentation, and, at the same time, to capture systemic features using equations. The approach is applied to norm emergence and internalisation in systems of learning agents. The logical formalism is rooted into a probabilistic defeasible logic instantiating Dung’s argumentation framework. (...) Rules of this logic are attached with probabilities to describe the agents’ minds and behaviours as well as uncertain environments. Then, the equation-based model for reinforcement learning, defined over this probability distribution, allows agents to adapt to their environment and self-organise. (shrink)

During its hundred-year history, Ludwig Wittgenstein’s Tractatus Logico-Philosophicus has undergone a variety of interpretations and explanations. But the significance of this work cannot be limited to an assessment of whether it had an impact on the development of logical positivism or not. Similarly, the reading of Tractatus cannot be reduced to just an ethical or some other readings. This article proposes to study a possible reading of “Tractatus” in terms of legal philosophy, which is based on the relation between (...) facts, values and norms, as well as on how interesting it could be (or would be) for legal philosophy. (shrink)

There is a deep tension between logical and probabilistic norms of belief. This article illustrates the normative force that is associated with these frameworks by showing how rather unrestricted belief bases can be improved by undergoing logical and probabilistic reflection. It is argued that probabilistic reasoning accounts for the reliability of the conclusions one can draw from the beliefs. Most importantly, reliability commands us to care for the increasing uncertainty of conjunctions of beliefs. Deductive logic captures the agent's commitment (...) towards all conclusions of her beliefs. In other words, it seems that commitment forces the agent to believe conclusions, which reliability tells her to view with scepticism. This conflict is resolved by arguing that commitment merely forces the agent to find the logical conclusions of her beliefs acceptable, not necessarily to believe them. This demands consistency but no deductive closure. Furthermore, it is shown that by restoring consistency, a straightforward connection between high subjective probability and full belief is undermined. Finally, the article delineates how this approach deals with the lottery paradox and the preface paradox. (shrink)

What is pedagogy, exactly? Merriam-Webster defines it simply as “the art, science, or profession of teaching.” In contemporary academic discourse, however, pedagogy is generally left undefined — with its apparent implicit meanings ranging anywhere from a specific “model for teaching” (e.g., behaviorist or progressivist instruction) to a broadly political philosophy of education in general (most famously, a “pedagogy of the oppressed”). In this paper, Norm Friesen and Hanno Su follow the Continental pedagogical tradition in giving pedagogy a general but (...) explicit definition. They do so by looking at how pedagogy arises both in everyday life and in school as unavoidably ethical activity undertaken primarily for the sake of the young person or child. Such activities, the authors maintain, are structured not so much by processes, methods, and outcomes, but by irresolvable oppositions and the tensions between them. They illustrate this inductively through a series of images and examples — moving gradually from ones involving parenting and early childhood to ones from elementary and secondary schooling. In this way, Friesen and Su show that pedagogy is not so much one or more ideologically focused or evidence-based instructional or psychological approaches to be mastered by a professional or teaching specialist. It is instead an independent but ethically informed practical perspective — one that can (and has) been extended to form a distinctively pedagogical theory and discipline. As such, it is something that is not only a part of our everyday life and culture, but arguably of all human cultures. (shrink)

This paper introduces deontic logic based on inquisitive semantics. A semantics for action formulas is introduced where each action formula is associated with a set of alternatives. Deontic operators are then interpreted as quantifying over all alternatives associated with the action formulas within their scope. It is shown how this construction provides solutions to problems related to free choice permissions and obligations, including issues concerning Hurford disjunctions. The main technical result is a complete axiomatization of the logic.

The present paper focuses on the phenomenon of normativity and genericity in language and cognition. More specifically, it investigates the use of normative generics, which are generalizations that state an ideal norm for a given category, in the context of norm breaching in parent-child interactions in English. This issue is researched by means of a specially designed questionnaire including 8 norm breaching parent-child interactions, which has been completed online by ca. 70 English-speaking female respondents. The paper uses (...) qualitative and quantitative methods to address two specific research issues. First, it compares the frequency of use of normative generics in norm breaching situations vis-à-vis the use of other types of normative linguistic expressions. Second, it analyses selected factors that are believed to favour the use of normative generics, including interactive openness of a given situation, norm salience, and perceived norm importance. Moreover, the paper sketches an explanatory model of normative generics that draws upon insights from the Conceptual Metonymy Theory, Construction Grammar, and Dual System Theory. (shrink)

A model of normative provisions and related axioms represented by using RDF/owl are presented as a contribution to implement the semantic web in the legal domain. In particular, a pattern able to implement the Hohfeldian legal fundamental relations between provisions using OWL-DL expressivity is proposed. Moreover, a query-based approach able to deal with relations between provision instances is described. An example of advanced access and reasoning over provisions using the proposed approach, as well as a prototype architecture of a (...) provision retrieval system, are shown. The main benefit is represented by the ability of the approach to keep the complexity of the problem within a description logic computational tractability. (shrink)

The debate on sustainable globalized development rests on two clearly stated economic assumptions: that "development" proceeds, solely and inevitably, through industrialization and the proliferation of capital intensive high-technology, towards the creation of service sector economies; and that globalization, based on a neoliberal, capitalist, free market ideology, provides the only vehicle for such development. Sustainability, according to the proponents of globalized development, is merely a function of market forces, which will generate the solutions for all problems including the environmental dilemmas (...) that loom over the globe today. The social focus of globalized development is clearly the "individual" and the much-touted goal of development in the context of these debates, is the emancipation of the individual from want. This glorification of the individual, so characteristic of the Enlightenment, has defined all aspects of modernity, leading to approaches that are self-focused and that give little thought to the needs of society or even the social context. The increasing impoverishment of human life and the growing environmental degradation, however, provide a poignant counterpoint to this onrush of capital interests, demanding a reassessment of sustainability separate from the logic of industrialization and globalized development. This paper examines the unfolding of the logic of capitalism, which underlies the structure of the Rostowian model of development and the problems in the assumptions underlying today''s globalized development process. The evident impossibility of sustainability in the current growth-based market system leads to the examination of alternatives including a reflexive understanding of the choices and the inclusion of opportunity costs, related to the social, environmental and economic aspects of decision making. The integration of all factors of production into the logic of development provides a sustainable alternative to the current system. (shrink)

The relation between logic and rationality has recently re-emerged as an important topic of discussion. Following the ideas of Broome [1999] and MacFarlane [2004], the debate focused on providing rational requirements, which work as bridges between logic and epistemic norms. However, as Broome [2014] and Way [2011] observed, the usual requirements cannot capture some important aspects of rationality, such as how one can rationally believe something on the basis of believing something else. Broome [2014] proposed a few additional (...) principles for this purpose. In this paper I develop a more systematic family of basing permissions using the recent notion of grounding. In particular, I claim that if Γ grounds A, and you believe Γ, then rationality permits you to believe A on the basis of believing Γ. (shrink)