Over the last decade there have been various attempts to use empirical data about people’s dispositions to choose to undermine various moral positions by arguing that our judgements about what to do are unreliable. Usually they are directed at non-consequentialists by consequentialists, but they have also been directed at all moral theories by skeptics about morality. Walter Sinnott-Armstrong has been one of the leading proponents of such general skepticism. He has argued that empirical results particularly undermine intuitionist moral epistemology. This (...) paper is an attempt to look at what intuitionists should say in response. Consider the following argument : Regress (R1) If any person S is ever justified in believing a normative claim that p then S must be able to infer p from other beliefs of S. (shrink)

This book defends a form of ethical intuitionism, according to which (i) there are objective moral truths; (ii) we know some of these truths through a kind of immediate, intellectual awareness, or "intuition"; and (iii) our knowledge of moral truths gives us reasons for action independent of our desires. The author rebuts all the major objections to this theory and shows that the alternative theories about the nature of ethics all face grave difficulties.

According to moral intuitionism, at least some moral seeming states are justification-conferring. The primary defense of this view currently comes from advocates of the standard account, who take the justification-conferring power of a moral seeming to be determined by its phenomenological credentials alone. However, the standard account is vulnerable to a problem. In brief, the standard account implies that moral knowledge is seriously undermined by those commonplace moral disagreements in which both agents have equally good phenomenological credentials supporting their (...) disputed moral beliefs. However, it is implausible to think that commonplace disagreement seriously undermines moral knowledge, and thus it is implausible to think that the standard account of moral intuitionism is true. (shrink)

Intuitionistic logic provides an elegant solution to the Sorites Paradox. Its acceptance has been hampered by two factors. First, the lack of an accepted semantics for languages containing vague terms has led even philosophers sympathetic to intuitionism to complain that no explanation has been given of why intuitionistic logic is the correct logic for such languages. Second, switching from classical to intuitionistic logic, while it may help with the Sorites, does not appear to offer any advantages when dealing with (...) the so-called paradoxes of higher-order vagueness. We offer a proposal that makes strides on both issues. We argue that the intuitionist’s characteristic rejection of any third alethic value alongside true and false is best elaborated by taking the normal modal system S4M to be the sentential logic of the operator ‘it is clearly the case that’. S4M opens the way to an account of higher-order vagueness which avoids the paradoxes that have been thought to infect the notion. S4M is one of the modal counterparts of the intuitionistic sentential calculus and we use this fact to explain why IPC is the correct sentential logic to use when reasoning with vague statements. We also show that our key results go through in an intuitionistic version of S4M. Finally, we deploy our analysis to reply to Timothy Williamson’s objections to intuitionistic treatments of vagueness. (shrink)

I argue that, given evidence of the factors that tend to distort our intuitions, ethical intuitionists should disown a wide range of common moral intuitions, and that they should typically give preference to abstract, formal intuitions over more substantive ethical intuitions. In place of the common sense morality with which intuitionism has traditionally allied, the suggested approach may lead to a highly revisionary normative ethics.

Walter Sinnott-Armstrong has developed and progressively refined an argument against moral intuitionism—the view on which some moral beliefs enjoy non-inferential justification. He has stated his argument in a few different forms, but the basic idea is straightforward. To start with, Sinnott-Armstrong highlights facts relevant to the truth of moral beliefs: such beliefs are sometimes biased, influenced by various irrelevant factors, and often subject to disagreement. Given these facts, Sinnott-Armstrong infers that many moral beliefs are false. What then shall we (...) think of our own moral beliefs? Either we have reason to think some of our moral beliefs are reliably formed or we have no such reason. If the latter, our moral beliefs are unjustified. If we have reason to think some moral beliefs are reliably formed, then those beliefs are not non-inferentially justified, because then we’ll have reason to accept something—namely, that they are reliably formed—that entails or supports those beliefs. But then, either way, our moral beliefs are not non-inferentially justified, and so moral intuitionism is false. This paper takes issue with Sinnott-Armstrong’s interesting and widely discussed argument, which we here call the Empirical Defeat Argument (EDA). According to us, the EDA does not defeat moral intuitionism. In section 1, we will set out the argument, briefly reviewing the rationale Sinnott-Armstrong offers for the premises. Then, in section 2, we identify a critical but dubious epistemological assumption concerning the nature of defeat that undergirds the argument. Finally, in section 3, we will defend our challenge to the EDA by answering two objections. (shrink)

Recent research on algebraic models of _quasi-Nelson logic_ has brought new attention to a number of classes of algebras which result from enriching (subreducts of) Heyting algebras with a special modal operator, known in the literature as a _nucleus_. Among these various algebraic structures, for which we employ the umbrella term _intuitionistic modal algebras_, some have been studied since at least the 1970s, usually within the framework of topology and sheaf theory. Others may seem more exotic, for their primitive operations (...) arise from algebraic terms of the intuitionistic modal language which have not been previously considered. We shall for instance investigate the variety of _weak implicative semilattices_, whose members are (non-necessarily distributive) meet semilattices endowed with a nucleus and an implication operation which is not a relative pseudo-complement but satisfies the postulates of Celani and Jansana’s strict implication. For each of these new classes of algebras we establish a representation and a topological duality which generalize the known ones for Heyting algebras enriched with a nucleus. (shrink)

This paper outlines and defends a moderate intuitionism. The point of departure is the intuitionism of W. D. Ross (1930) in The Right and the Good, conceived as ethically pluralist and epistemologically rationalist. The paper articulates a conception of self-evidence – including mediate as well as immediate kinds – appropriate to a moderate intuitionism, explores some of the resources and varieties of that position, and considers some problems and prospects for a rationalist version of intuitionism. The (...) final section addresses the issue of how best to conceive the nature and grounds of prima facie duty, the problem of whether intuitionism can adequately deal with conflicts of prima facie duties, and the question of how satisfactorily a moderate intuitionism can account for the epistemic status of moral judgments of overall duty and their connection with rational action. (shrink)

We review the state of the art in moral psychology to answer 6 questions: 1) Where do moral beliefs and motivations come from? 2) How does moral judgment work? 3) What is the evidence for the social intuitionist model? 4) What exactly are the moral intuitions? 5) How does morality develop? And 6) Why do people vary in their morality? We describe the intuitionist approach to moral psychology. The mind makes rapid affective evaluations of everything it encounters, and these evaluations (...) (intuitions) shape and push subsequent moral reasoning. This approach to moral judgment has a variety of implications for moral philosophy and for the law in that it questions common assumptions about the reliability and causal efficacy of private, conscious reasoning. (shrink)

The present work is motivated by two questions. (1) What should an intuitionistic epistemic logic look like? (2) How should one interpret the knowledge operator in a Kripke-model for it? In what follows we outline an answer to (2) and give a model-theoretic definition of the operator K. This will shed some light also on (1), since it turns out that K, defined as we do, fulfills the properties of a necessity operator for a normal modal logic. The interest of (...) our construction also lies in a better insight into the intuitionistic solution to Fitch's paradox, which is discussed in the third section. In particular we examine, in the light of our definition, De Vidi and Solomon's proposal of formulating the verification thesis as Φ → ¬¬KΦ. We show, as our main result, that this definition excapes the paradox, though it is validated only under restrictive conditions on the models. (shrink)

The aims of this paper are twofold: firstly, to say something about that philosophy of mathematics known as 'intuitionism' and, secondly, to fit these remarks into a more general message for the philosophy of mathematics as a whole. What I have to say on the first score can, without too much inaccuracy, be compressed into two theses. The first is that the intuitionistic critique of classical mathematics can be seen as based primarily on epistemological rather than on meaning-theoretic considerations. (...) The second is that the intuitionist's chief objection to the classical mathematician's use of logic does not center on the use of particular logical principles (in particular, the law of excluded middle and its ilk). Rather on the role the classical mathematician assigns (or at least extends) generally (i.e. regardless of the particular principles used) to the use of logic in the production mathematical proofs. Thus, the intuitionist critique of logic that we shall be presenting is far more radical than that which has commonly been presented. -/- Concerning the second, more general, theme, my claim is this: some restriction of the role of logical inference in mathematical proof such as that mentioned above is necessary if one is to account for the seeming difference in the epistemic conditions of provers whose reasoning is based on genuine insight into the subject-matter being investigated, and would-be provers whose reasoning is based not on such insight, but rather on principles of inference which hold of every subject-matter indifferently. (shrink)

Thinking about morality -- Story of contemporary intuitionism -- Moral knowledge -- New challenges to intuitionism -- Grounds of morality -- Right and the good reconsidered -- Intuitionism's rivals -- Being moral: how and why.

The purpose of this paper is to define a new logic $${\mathcal {SI}}$$ called semi-intuitionistic logic such that the semi-Heyting algebras introduced in [ 4 ] by Sankappanavar are the semantics for $${\mathcal {SI}}$$ . Besides, the intuitionistic logic will be an axiomatic extension of $${\mathcal {SI}}$$.

Conditional logics have traditionally been intended to formalize various intuitively correct modes of reasoning involving conditional expressions in natural language. Although conditional logics have by now been thoroughly studied in a classical context, they have yet to be systematically examined in an intuitionistic context, despite compelling philosophical and technical reasons to do so. This paper addresses this gap by thoroughly examining the basic intuitionistic conditional logic ICK, the intuitionistic counterpart of Chellas’ important classical system CK. I give ICK both worlds (...) semantics and algebraic semantics, and prove that these are equivalent. I give a Gödel-type embedding of ICK into CK and a Glivenko-type embedding of CK into ICK. I axiomatize ICK and prove soundness, completeness, and decidability results. Finally, I discuss extending ICK. (shrink)

This paper is a reaction to the following remark by grzegorczyk: "the compound sentences are not a product of experiment. they arise from reasoning. this concerns also negations; we see that the lemon is yellow, we do not see that it is not blue." generally, in science the truth is ascertained as indirectly as falsehood. an example: a litmus-paper is used to verify the sentence "the solution is acid." this approach gives rise to a (very intuitionistic indeed) conservative extension of (...) the heyting logic satisfying natural duality laws. (shrink)

Brouwer's views on the foundations of mathematics have inspired the study of intuitionistic logic, including the study of the intuitionistic propositional calculus and its extensions. The theory of these systems has become an independent branch of logic with connections to lattice theory, topology, modal logic and other areas. This paper aims to present a modern account of semantics for intuitionistic propositional systems. The guiding idea is that of a hierarchy of semantics, organized by increasing generality: from the least general Kripke (...) semantics on through Beth semantics, topological semantics, Dragalin semantics, and finally to the most general algebraic semantics. While the Kripke, topological, and algebraic semantics have been extensively studied, the Beth and Dragalin semantics have received less attention. We bring Beth and Dragalin semantics to the fore, relating them to the concept of a nucleus from pointfree topology, which provides a unifying perspective on the semantic hierarchy. (shrink)

In this paper, I defend a non-skeptical intuitionist approach to moral epistemology from recent criticisms. Starting with Sinnott-Armstrong's skeptical attacks, I argue that a familiar sort of skeptical argument rests on a problematic conception of the evidential grounds of our moral judgments. The success of his argument turns on whether we conceive of the evidential grounds of our moral judgments as consisting entirely of non-normative considerations. While we cannot avoid skepticism if we accept this conception of our evidential grounds, that's (...) because accepting this conception of our evidential grounds is tantamount to accepting the skeptic's conclusion. We have nothing to fear from arguments for skepticism from skepticism. (shrink)

In the recent metaethical literature there has been significant interest in the prospects for what I am denoting ‘Perceptual Intuitionism’: the view that normal ethical agents can and do have non-inferential justification for first-order ethical beliefs by having ethical perceptual experiences, e.g., Cullison 2010, McBrayer 2010, Vayrynen 2008. If true, it promises to constitute an independent a posteriori intuitionist epistemology, providing an alternative to intuitionist accounts which posit a priori intuition and/or emotion as sources of non-inferentially justified ethical beliefs. (...) As it is formulated, it is plausible that a necessary con- dition for the view is the truth of Ethical Perception: normal ethical agents can and do have perceptual experiences as of the instantiation of ethical properties. In this paper a sophisticated and promising account of Ethical Perception is offered. Extant objections are shown to fail. However, it will be argued that it is far from obvious that the account of Perceptual Intuitionism which emerges constitutes an independent alternative to other intuitionist accounts. This is because we have reason to think that ethical perceptual experience may be epistemically dependent on other epistemic sources, e.g. a priori intuition or emotion. (shrink)

The Gödel translation provides an embedding of the intuitionistic logic$\mathsf {IPC}$into the modal logic$\mathsf {Grz}$, which then embeds into the modal logic$\mathsf {GL}$via the splitting translation. Combined with Solovay’s theorem that$\mathsf {GL}$is the modal logic of the provability predicate of Peano Arithmetic$\mathsf {PA}$, both$\mathsf {IPC}$and$\mathsf {Grz}$admit provability interpretations. When attempting to ‘lift’ these results to the monadic extensions$\mathsf {MIPC}$,$\mathsf {MGrz}$, and$\mathsf {MGL}$of these logics, the same techniques no longer work. Following a conjecture made by Esakia, we add an appropriate version (...) of Casari’s formula to these monadic extensions (denoted by a ‘+’), obtaining that the Gödel translation embeds$\mathsf {M^{+}IPC}$into$\mathsf {M^{+}Grz}$and the splitting translation embeds$\mathsf {M^{+}Grz}$into$\mathsf {MGL}$. As proven by Japaridze, Solovay’s result extends to the monadic system$\mathsf {MGL}$, which leads us to a provability interpretation of both$\mathsf {M^{+}IPC}$and$\mathsf {M^{+}Grz}$. (shrink)

Hybrid logics are a principled generalization of both modal logics and description logics, a standard formalism for knowledge representation. In this paper we give the first constructive version of hybrid logic, thereby showing that it is possible to hybridize constructive modal logics. Alternative systems are discussed, but we fix on a reasonable and well-motivated version of intuitionistic hybrid logic and prove essential proof-theoretical results for a natural deduction formulation of it. Our natural deduction system is also extended with additional inference (...) rules corresponding to conditions on the accessibility relations expressed by so-called geometric theories. Thus, we give natural deduction systems in a uniform way for a wide class of constructive hybrid logics. This shows that constructive hybrid logics are a viable enterprise and opens up the way for future applications. (shrink)

We show that, if a suitable intuitionistic metatheory proves that consistency implies satisfiability for subfinite sets of propositional formulas relative either to standard structures or to Kripke models, then that metatheory also proves every negative instance of every classical propositional tautology. Since reasonable intuitionistic set theories such as HAS or IZF do not demonstrate all such negative instances, these theories cannot prove completeness for intuitionistic propositional logic in the present sense.

The aim of this paper is to establish a phenomenological mathematical intuitionism that is based on fundamental phenomenological-epistemological principles. According to this intuitionism, mathematical intuitions are sui generis mental states, namely experiences that exhibit a distinctive phenomenal character. The focus is on two questions: what does it mean to undergo a mathematical intuition and what role do mathematical intuitions play in mathematical reasoning? While I crucially draw on Husserlian principles and adopt ideas we find in phenomenologically minded mathematicians (...) such as Hermann Weyl and Kurt Gödel, the overall objective is systematic in nature: to offer a plausible approach towards mathematics. (shrink)

Ethical Intuitionism was the dominant moral theory in Britain for much of the 18th, 19th and the first third of the twentieth century. However, during the middle decades of the twentieth century ethical intuitionism came to be regarded as utterly untenable. It was thought to be either empty, or metaphysically and epistemologically extravagant, or both. This hostility led to a neglect of the central intuitionist texts, and encouraged the growth of a caricature of intuitionism that could easily (...) be rejected before moving on to 'more serious' philosophical theories. More recently, however, this hostility towards ethical intuitionism has subsided. A wide range of moral philosophers, from Aristotelians, to rule-consequentialists, to expressivists, Kantians and deontologists, are beginning to look to the ethical intuitionists's work as a positive resource. It is, therefore, a good time to get clear on what it was that intuitionists said, and re-evaluate their contribution to our understanding of morality. This volume is the first serious engagement with ethical intuitionism in the light of contemporary developments in ethical theory. It contains essays by eminent moral philosophers working in very different traditions whose aim is to clarify and assess ethical intuitionism. Issues addressed include whether the plurality of basic principles intuitionists adhere to can be grounded in some more fundamental principle; the autonomy of ethics and self-evidence; moral realism and internalism; and the open question argument and naturalism. (shrink)

This is a long-awaited new edition of one of the best known Oxford Logic Guides. The book gives an introduction to intuitionistic mathematics, leading the reader gently through the fundamental mathematical and philosophical concepts. The treatment of various topics, for example Brouwer's proof of the Bar Theorem, valuation systems, and the completeness of intuitionistic first-order logic, have been completely revised.

It is a central tenet of ethical intuitionism as defended by W. D. Ross and others that moral theory should reflect the convictions of mature moral agents. Hence, intuitionism is plausible to the extent that it corresponds to our well-considered moral judgments. After arguing for this claim, I discuss whether intuitionists offer an empirically adequate account of our moral obligations. I do this by applying recent empirical research by John Mikhail that is based on the idea of a (...) universal moral grammar to a number of claims implicit in W. D. Ross’s normative theory. I argue that the results at least partly vindicate intuitionism. (shrink)

Bi-intuitionistic logic is the result of adding the dual of intuitionistic implication to intuitionistic logic. In this note, we characterize the expressive power of this logic by showing that the first order formulas equivalent to translations of bi-intuitionistic propositional formulas are exactly those preserved under bi-intuitionistic directed bisimulations. The proof technique is originally due to Lindstrom and, in contrast to the most common proofs of this kind of result, it does not use the machinery of neither saturated models nor elementary (...) chains. (shrink)

Covering moral intuition, self-evidence, non-inferentiality, moral emotion and seeming states, Hossein Dabbagh defends the epistemology of moral intuitionism. His line of analysis resists the empirical challenges derived from empirical moral psychology and reveals the seeming-based account of moral intuitionism as the most tenable one. The Moral Epistemology of Intuitionism combines epistemological intuitionism with work in neuroethics to develop an account of the role that moral intuition and emotion play in moral judgment. The book culminates in a (...) convincing argument about the value of understanding moral intuitionism in terms of intellectual seeming and perceptual experience. (shrink)

Hume bequeathed to rational intuitionists a problem concerning moral judgment and the will – a problem of sufficient severity that it is still cited as one of the major reasons why intuitionism is untenable.1 Stated in general terms, the problem concerns how an intuitionist moral theory can account for the intimate connection between moral judgment and moral motivation. One reason that this is still considered to be a problem for intuitionists is that it is widely assumed that the early (...) intuitionists made little progress towards solving it. In this essay, I wish to challenge this assumption by examining one of the more subtle intuitionist responses to Hume, viz., that offered by Thomas Reid. For reasons that remain unclear to me, Reid's response to Hume on this issue has been almost entirely neglected. I shall argue that it is nonetheless one that merits our attention, for at least two reasons. In the first place, Reid's response to Hume's challenge to rational intuitionism bears a close affinity to the type of response that he offers to Hume's broadly skeptical challenge to realist views regarding our perception of the external world. Since Reid's strategy in the latter case is widely regarded as exhibiting significant promise, it is natural to wonder whether, when applied to the moral domain, this type of strategy displays similar promise.2 I will suggest that it does. That is, I will suggest that since Reid's broadly nativist position in perception is one well worth considering, then so also is his broadly nativist account of moral motivation. Second, Reid's position regarding moral motivation represents an intriguing attempt to blend a broadly intuitionist view with important insights from the sentimentalist tradition. In this respect, Reid's view is a genuine hybrid position unlike that offered by other intuitionists such as Richard Price. The synthetic character of Reid's position, I claim, gives it a unique type of theoretical richness, since it incorporates some very attractive features of both rational intuitionism and sentimentalism. (shrink)

In this paper it is shown that the intuitionistic .xed point theory equation image for α times iterated fixed points of strictly positive operator forms is conservative for negative arithmetic and equation image sentences over the theory equation image for α times iterated arithmetic comprehension without set parameters.This generalizes results previously due to Buchholz [5] and Arai [2].

We consider notions of boundedness of subsets of the natural numbers ℕ that occur when doing mathematics in the context of intuitionistic logic. We obtain a new characterization of the notion of a pseudobounded subset and we formulate the closely related notion of a detachably finite subset. We establish metric equivalents for a subset of ℕ to be detachably finite and to satisfy the ascending chain condition. Following Ishihara, we spell out the relationship between detachable finiteness and sequential continuity. Most (...) of the results do not require countable choice. (shrink)

Dijkstra and Scholten have proposed a formalization of classical predicate logic on a novel deductive system as an alternative to Hilbert's style of proof and Gentzen's deductive systems. In this context we call it CED (Calculus of Equational Deduction). This deductive method promotes logical equivalence over implication and shows that there are easy ways to prove predicate formulas without the introduction of hypotheses or metamathematical tools such as the deduction theorem. Moreover, syntactic considerations (in Dijkstra's words, "letting the symbols do (...) the work") have led to the "calculational style," an impressive array of techniques for elegant proof constructions. In this paper, we formalize intuitionistic predicate logic according to CED with similar success. In this system (I-CED), we prove Leibniz's principle for intuitionistic logic and also prove that any (intuitionistic) valid formula of predicate logic can be proved in I-CED. (shrink)

The geometric system of deduction called N-Graphs was introduced by de Oliveira in 2001. The proofs in this system are represented by means of digraphs and, while its derivations are mostly based on Gentzen's sequent calculus, the system gets its inspiration from geometrically based systems, such as the Kneales' tables of development, Statman's proofs-as-graphs, Buss' logical flow graphs, and Girard's proof-nets. Given that all these geometric systems appeal to the classical symmetry between premises and conclusions, providing an intuitionistic version of (...) any of these is an interesting exercise in extending the range of applicability of the geometric system in question. In this article we produce an intuitionistic version of N-Graphs, based on Maehara's LJ' system, as described by Takeuti. Recall that LJ' has multiple conclusions in all but the essential intuitionistic rules, e.g., implication right and negation right. We show soundness and completeness of our intuitionistic N-Graphs with respect to LJ'. We also discuss how we expect to extend this work to a version of N-Graphs corresponding to the intuitionistic logic system FIL (Full Intuitionistic Logic) of de Paiva and Pereira and sketch future developments. (shrink)

Fuzzy intuitionistic quantum logics (called also Brouwer-Zadeh logics) represent to non standard version of quantum logic where the connective not is split into two different negation: a fuzzy-like negation that gives rise to a paraconsistent behavior and an intuitionistic-like negation. A completeness theorem for a particular form of Brouwer-Zadeh logic (BZL 3) is proved. A phisical interpretation of these logics can be constructed in the framework of the unsharp approach to quantum theory.

There are several open problems in the study of the calculi which result from adding either of Hilbert's ϵ- or τ-operators to the first order intuitionistic predicate calculus. This paper provides answers to several of them. In particular, the first complete and sound semantics for these calculi are presented, in both a “quasi-extensional” version which uses choice functions in a straightforward way to interpret the ϵ- or τ-terms, and in a form which does not require extensionality assumptions. Unlike the classical (...) case, the addition of either operator to intuitionistic logic is non-conservative. Several interesting consequences of the addition of each operator are proved. Finally, the independence of several other schemes in either calculus are also proved, making use of the semantics supplied earlier in the paper. (shrink)

In this paper we give a brief treatment of a theory of proofs for a system of Full Intuitionistic Linear Logic. This system is distinct from Classical Linear Logic, but unlike the standard Intuitionistic Linear Logic of Girard and Lafont includes the multiplicative disjunction par. This connective does have an entirely natural interpretation in a variety of categorical models of Intuitionistic Linear Logic. The main proof-theoretic problem arises from the observation of Schellinx that cut elimination fails outright for an intuitive (...) formulation of Full Intuitionistic Linear Logic; the nub of the problem is the interaction between par and linear implication. We present here a term assignment system which gives an interpretation of proofs as some kind of non-deterministic function. In this way we find a system which does enjoy cut elimination. The system is a direct result of an analysis of the categorical semantics, though we make an effort to present the system as if it were purely a proof-theoretic construction. (shrink)

The study of moral decision-making presents to us two approaches for understanding such choices. The cognitive and the neurocognitive approaches postulate that reason and reasoning determines moral judgments. On the other hand, the intuitionist approaches postulate that automated intuitions mostly dominate moral judgments. There is a growing concern that neither of these approaches by itself captures all the key aspects of moral judgments. This paper draws on models from neurocognitive research and social-intuitionist research areas to propose an integrative cognitive–intuitive model (...) of moral decision-making. The model suggests that moral decision-making includes five interdependent, yet functionally distinct steps, issue framing, pre-processing, moral judgment, moral reflection, and moral intent. The model proposes a cognitive–intuitive view of moral judgment and it describes how emotion regulation, perceived moral intensity, and perceived ethical climate constructs impact the formation of moral intent. The paper discusses the theories that link emotions to moral judgment and implications of the model for future research and its implication for managers. (shrink)

Motivated by the definition of semi-Nelson algebras, a propositional calculus called semi-intuitionistic logic with strong negation is introduced and proved to be complete with respect to that class of algebras. An axiomatic extension is proved to have as algebraic semantics the class of Nelson algebras.

This chapter examines the debate between advocates of classical logic and advocates of intuitionistic logic. It examines the semantic and epistemic issues on which this debate is usually conducted. After introducing the idea that logic is a model of correct reasoning, the chapter explores the viability of a logic intermediate between classical and intuitionistic.

We propose the beginnings of an intuitionistic propopsitional dynamic logic, and describe several serious open problems.

Let T be a first-order theory. A T-normal Kripke structure is one in which every world is a classical model of T. This paper gives a characterization of the intuitionistic theory T of sentences intuitionistically valid in all T-normal Kripke structures and proves the corresponding soundness and completeness theorems. For Peano arithmetic , the theory PA is a proper subtheory of Heyting arithmetic , so HA is complete but not sound for PA-normal Kripke structures.