A Non-deterministic View on Non-classical Negations

We investigate two large families of logics, differing from each other by the treatment of negation. The logics in one of them are obtained from the positive fragment of classical logic (with or without a propositional constant ff for “the false”) by adding various standard Gentzen-type rules for negation. The logics in the other family are similarly obtained from LJ⁺, the positive fragment of intuitionistic logic (again, with or without ff). For all the systems, we provide simple semantics which is based on non-deterministic four-valued or three-valued structures, and prove soundness and completeness for all of them. We show that the role of each rule is to reduce the degree of non-determinism in the corresponding systems. We also show that all the systems considered are decidable, and our semantics can be used for the corresponding decision procedures. Most of the extensions of LJ⁺ (with or without ff) are shown to be conservative over the underlying logic, and it is determined which of them are not.     

Logical equations and admissible rules of inference with parameters in modal provability logics

This paper concerns modal logics of provability — Gödel-Löb systemGL and Solovay logicS — the smallest and the greatest representation of arithmetical theories in propositional logic respectively. We prove that the decision problem for admissibility of rules (with or without parameters) inGL andS is decidable. Then we get a positive solution to Friedman's problem forGL andS. We also show that A. V. Kuznetsov's problem of the existence of finite basis for admissible rules forGL andS has a negative solution. Afterwards we give an algorithm deciding the solvability of logical equations inGL andS and constructing some solutions.     

An encompassing framework for Paraconsistent Logic Programs

We propose a framework which extends Antitonic Logic Programs [Damásio and Pereira, in: Proc. 6th Int. Conf. on Logic Programming and Nonmonotonic Reasoning, Springer, 2001, p. 748] to an arbitrary complete bilattice of truth-values, where belief and doubt are explicitly represented. Inspired by Ginsberg and Fitting's bilattice approaches, this framework allows a precise definition of important operators found in logic programming, such as explicit and default negation. In particular, it leads to a natural semantical integration of explicit and default negation through the Coherence Principle [Pereira and Alferes, in: European Conference on Artificial Intelligence, 1992, p. 102], according to which explicit negation entails default negation. We then define Coherent Answer Sets, and the Paraconsistent Well-founded Model semantics, generalizing many paraconsistent semantics for logic programs. In particular, Paraconsistent Well-Founded Semantics with eXplicit negation (WFSX_p) [Alferes et al., J. Automated Reas. 14 (1) (1995) 93–147; Damásio, PhD thesis, 1996]. The framework is an extension of Antitonic Logic Programs for most cases, and is general enough to capture Probabilistic Deductive Databases, Possibilistic Logic Programming, Hybrid Probabilistic Logic Programs, and Fuzzy Logic Programming. Thus, we have a powerful mathematical formalism for dealing simultaneously with default, paraconsistency, and uncertainty reasoning. Results are provided about how our semantical framework deals with inconsistent information and with its propagation by the rules of the program.     

Some definitions of negation leading to paraconsistent logics

In positive logic the negation of a propositionA is defined byA X whereX is some fixed proposition. A number of standard properties of negation, includingreductio ad absurdum, can then be proved, but not the law of noncontradiction so that this forms a paraconsistent logic. Various stronger paraconsistent logics are then generated by putting in particular propositions forX. These propositions range from true through contingent to false.     

Standard and non-standard Newcomb Problems

Examples involving common causes — most prominently, examples involving genetically influenced choices — are analytically equivalent not to standard Newcomb Problems — in which the Predictor genuinely predicts the agent's decision — but to non-standard Newcomb Problems — in which the Predictor guarantees the truth of her predictions by interfering with the agent's decision to make the agent choose as it was predicted she would. When properly qualified, causal and epistemic decision theories diverge only on standard — not on non-standard — Newcomb Problems, and thus not on examples involving common causes.     

All Brutes are Subhuman: Aristotle and Ockham on Private Negation

The mediaeval logic of Aristotelian privation, represented by Ockham's expositionof All A is non-P as All S is of a type T that is naturally P and no S is P, iscritically evaluated as an account of privative negation. It is argued that there aretwo senses of privative negation: (1) an intensifier (as in subhuman), the dualof Neoplatonic hypernegation (superhuman), which is studied in linguistics asan operator on scalar adjectives, and (2) a (often lexicalized) Boolean complementrelative to the extension of a privative negation in sense (1) (e.g., Brute). Thissecond sense, which is the privative negation discussed in modern linguistics, isshown to be Aristotle's. It is argued that Ockham's exposition fails to capture muchof the logic of Aristotelian privation due to limitations in the expressive power of thesyllogistic.     

Formalising the informal?: Dynamic social order, bottom-up social control, and spontaneous normative relations

The right framework for studying normative issues in infosociety and MAS is that of deliberate or spontaneous social order, and intended or unintended, centralised or decentralised forms of social control. For effectively supporting human cooperation it is necessary to “incorporate” social and normative knowledge in intelligent technology; computers should deal with—and thus partially “understand”—permissions, obligations, power, roles, commitments, trust, etc. Here only one facet of this problem is considered: the spontaneous and decentralised norm creation, and normative monitoring and intervention. Cognitive aspects of spontaneous conventions, implicit commitments, tacit agreements, and the bottom-up issuing and spreading of norms are discussed. The transition from “face to face” normative relationships to some stronger constraints on agents' action, and to institutions and authority, and the possibility of a consequent increase of trust, are explored. In particular, I focus on the transition from two party trust, right, permission, and commitment, to three party relationships, where some witness or some enforcing authority is introduced. In this perspective of ‘formalising the informal’, i.e., the interpersonal unofficial normative matter, I discuss (also in order to stress dangers of computer-based formalisation and enforcement of rules) the important phenomenon of functional (collaborative) systematic violation of rules in organisation and cooperation, and the possible emergence of a “convention to violate”.     

Yes,Virginia, there Really are Paraconsistent Logics

B. H. Slater has argued that there cannot be any truly paraconsistent logics, because it's always more plausible to suppose whatever negation symbol is used in the language is not a real negation, than to accept the paraconsistent reading. In this paper I neither endorse nor dispute Slater's argument concerning negation; instead, my aim is to show that as an argument against paraconsistency, it misses (some of) the target. A important class of paraconsistent logics — the preservationist logics — are not subject to this objection. In addition I show that if we identify logics by means of consequence relations, at least one dialetheic logic can be reinterpreted in preservationist (non-dialetheic) terms. Thus the interest of paraconsistent consequence relations — even those that emerge from dialetheic approaches — does not depend on the tenability of dialetheism. Of course, if dialetheism is defensible, then paraconsistent logic will be required to cope with it. But the existence (and interest) of paraconsistent logics does not depend on a defense of dialetheism.     

Hegel's Glutty Negation

Some authors have claimed that Hegel's ‘determinate negation’ should be distinguished from ‘logical’ or ‘formal’ negation, that is, from a view of negation as a contradictory forming operator. In contrast, I argue that dialectical determinate negation involves a view of negation as a contradictory forming operator, and can therefore count as formal negation in every respect. However, as it is clear in contemporary glutty semantics of negation, one may distinguish between different accounts of the relationship between negation, contradiction and content. I suggest that, differently from classical negation, and as glutty negation, dialectical negation has partial content.     

Ethos,pathos and logos in Aristotle's Rhetoric: A re-examination

In Aristotle's Rhetoric, logos must be conceived as enthymematical argumentation relative to the issue of the case. Ethos and pathos also can take the form of an enthymeme, but this argumentation doesn't relate (directly) to the issue. In this kind of enthymeme, the conclusion is relative to the ethos of the speaker or (reasons for) the pathos of the audience. In an ideal situation — with a good procedure and rational judges — logos dominates and in the real situation of Aristotle's time — with an imperfect procedure and irrational judges — ethos and pathos prevail.I should like to thank R. Berkenbosch and J. Wisse for their comments.     

Converse Ackermann Croperty and semiclassical negation

A prepositional logic S has the Converse Ackermann Property (CAP) if (AB)C is unprovable in S when C does not contain . In A Routley-Meyer semantics for Converse Ackermann Property (Journal of Philosophical Logic, 16 (1987), pp. 65–76) I showed how to derive positive logical systems with the CAP. There I conjectured that each of these positive systems were compatible with a so-called semiclassical negation. In the present paper I prove that this conjecture was right. Relational Routley-Meyer type semantics are provided for each one of the resulting systems (the positive systems plus the semiclassical negation).     

On the devalued self and implications for treatment

A survey of the self theories of several illustrious clinicians suggests that—despite its increasing interest for contemporary dynamic psychotherapists —a holistic self psychology has little practical utility. Rather, it is a variant of structural theory, involving a component of a nontraditional structure of the self, that appears to be of the most practical use. Therapy in this mode combines both steadfast positive regard and planful functioning of the therapist as a beneficial model or ideal image.     

The logic of causal methods in social science

Two kinds of causal inference rules which are widely used by social scientists are investigated. Two conceptions of causation also widely used are explicated — the INUS and probabilistic conceptions of causation. It is shown that the causal inference rules which link correlation, a kind of partial correlation, and a conception of causation areinvalid. It is concluded anew methodology is required for causal inference.     

Fuzzy intuitionistic quantum logics

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.     

Accidentally True Belief and Warrant

The Proper Functionist account of warrant – like many otherexternalist accounts – is vulnerable to certain Gettier-style counterexamples involving accidentally true beliefs. In this paper, I briefly survey the development of the account, noting the way it was altered in response to such counterexamples. I then argue that Alvin Plantinga's latest amendment to the account is flawed insofar as it rules out cases of true beliefs which do intuitively strike us as knowledge, and that a conjecture recently put forward by Thomas Crisp is also defective. I conclude by presenting my own suggestion as to how the account can be made less vulnerable to counterexamples involving accidentally true beliefs. Although I stay within the confines of Proper Functionism here, I think that my proposal (modulo a few details) could be attached to other externalist accounts of warrant as well.     

Formal systems of dialogue rules

Section 1 contains a survey of options in constructing a formal system of dialogue rules. The distinction between material and formal systems is discussed (section 1.1). It is stressed that the material systems are, in several senses, formal as well. In section 1.2 variants as to language form (choices of logical constants and logical rules) are pointed out. Section 1.3 is concerned with options as to initial positions and the permissibility of attacks on elementary statements. The problem of ending a dialogue, and of infinite dialogues, is treated in section 1.4. Other options, e.g., as to the number of attacks allowed with respect to each statement, are listed in section 1.5. Section 1.6 explains the concept of a chain of arguments.From section 2 onward four types of dialectic systems are picked out for closer study: D, E, Di and Ei. After a preliminary section on dialogue sequents and winning strategies, the equivalence of derivability in intuitionistic logic and the existence of a winning strategy (for the Proponent) on the strength of Ei is shown by simple inductive proofs.Section 3 contains a — relatively quick — proof of the equivalence of the four systems. It follows that each of them yields intuitionistic logic.     

Complex Genetic Disorders: Evaluating When Genetic Research Findings Are Applicable for Genetic Counseling Practice

Traditional genetic counseling processes and principles will be extended to a new realm—complex disorders. Although it may seem like a daunting task, understanding the methodologies used to study complex genetic disorders will enable genetic counselors to critically analyze research studies involving complex disorders. In this article, we explain newly evolving methodologies for genetic research, including case-control studies and transmission disequilibrium testing (TDT). Additionally, a framework is provided for evaluating original research findings and replication studies.     

Jealousy,Shame, and the Rival

This essay is a critique of the two chapters on jealousy in Jerome Neu's book A Tear is an Intellectual Thing. The rival — as anobject of both fear and hatred — is of central importance in romantic jealousy, but it is here argued that the role of the rival cannot be fully understood in Neu's account of jealousy and that shame (not noted by Neu) must be seen as central to the concept of jealousy if the role of the rival is to be fully understood.     

Negation: A theory of its meaning,representation, and use

This article presents a model-based theory of what negation means, how it is mentally represented, and how it is understood. The theory postulates that negation takes a single argument that refers to a set of possibilities and returns the complement of that set. Individuals therefore tend to assign a small scope to negation in order to minimize the number of models of possibilities that they have to consider. Individuals untrained in logic do not know the possibilities corresponding to the negation of compound assertions formed with if, or, and and, and have to infer the possibilities one by one. It follows that negations are easier to understand, and to formulate, when individuals already have in mind the possibilities to be negated. The paper shows that the evidence, including the results of recent studies, corroborates the theory.