Logical matrices and the amalgamation property

The main result of the present paper — Theorem 3 — establishes the equivalence of the interpolation and amalgamation properties for a large family of logics and their associated classes of matrices.     

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.     

A verification framework for agent programming with declarative goals

A long and lasting problem in agent research has been to close the gap between agent logics and agent programming frameworks. The main reason for this problem of establishing a link between agent logics and agent programming frameworks is identified and explained by the fact that agent programming frameworks have hardly incorporated the concept of a declarative goal. Instead, such frameworks have focused mainly on plans or goals-to-do instead of the end goals to be realised which are also called goals-to-be. In this paper, the programming language GOAL is introduced which incorporates such declarative goals. The notion of a commitment strategy—one of the main theoretical insights due to agent logics, which explains the relation between beliefs and goals—is used to construct a computational semantics for GOAL. Finally, a proof theory for proving properties of GOAL agents is introduced. Thus, the main contribution of this paper, rather than the language GOAL itself, is that we offer a complete theory of agent programming in the sense that our theory provides both for a programming framework and a programming logic for such agents. An example program is proven correct by using this programming logic.     

Modal Incompleteness Revisited

In this paper, we are going to analyze the phenomenon of modal incompleteness from an algebraic point of view. The usual method of showing that a given logic L is incomplete is to show that for some L and some cannot be separated from by a suitably wide class of complete algebras — usually Kripke algebras. We are going to show that classical examples of incomplete logics, e.g., Fine logic, are not complete with respect to any class of complete BAOs. Even above Grz it is possible to find a continuum of such logics, which immediately implies the existence of a continuum of neighbourhood-incomplete Grz logics. Similar results can be proved for Löb logics. In addition, completely incomplete logics above Grz may be found uniformly as a result of failures of some admissible rule of a special kind.     

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.     

Pretabular varieties of modal algebras

We study modal logics in the setting of varieties of modal algebras. Any variety of modal algebras generated by a finite algebra — such, a variety is called tabular — has only finitely many subvarieties, i.e. is of finite height. The converse does not hold in general. It is shown that the converse does hold in the lattice of varieties of K4-algebras. Hence the lower part of this lattice consists of tabular varieties only. We proceed to show that there is a continuum of pretabular varieties of K4-algebras — those are the non-tabular varieties all of whose proper subvarieties are tabular — in contrast with Maksimova's result that there are only five pretabular varieties of S4-algebras.     

The Ambiguity of Quantifiers

In the tradition of substructural logics, it has been claimed for a long time that conjunction and inclusive disjunction are ambiguous:we should, in fact, distinguish between ‘lattice’ connectives (also called additive or extensional) and ‘group’ connectives (also called multiplicative or intensional). We argue that an analogous ambiguity affects the quantifiers. Moreover, we show how such a perspective could yield solutions for two well-known logical puzzles: McGee’s counterexample to modus ponens and the lottery paradox.     

Merging without mystery or: Variables in dynamics semantics

In this paper we discuss the treatment of variables in dynamic semantics. Referent systems are introduced as a flexible mechanism for working with variables. In a referent system we carefully distinguish the variables themselves both from the machinery by which we manipulate them — their names — and from the information that we store in them — their values. It is shown that the referent systems provide a natural basis for dynamic semantics. The semantics with referent systems is compared with the familiar formalisms in dynamic semantics,DRT andDPL.     

Information functions with applications

In the first place, we present the definition and fundamental properties of information functions — functions which establish a correspondence between sets of formulas and the information contained in them. The intuitions for the notion of information stem from the conception of Bar-Hillel and Carnap in [3]. In § 2 we will briefly show how those notions can be applied to the logic of theory change. In § 3 we will use them for proving two theorems about the lattices of classical subtheories and their content.     

Action negation and alternative reductions for dynamic deontic logics

Dynamic deontic logics reduce normative assertions about explicit complex actions to standard dynamic logic assertions about the relation between complex actions and violation conditions. We address two general, but related problems in this field. The first is to find a formalization of the notion of ‘action negation’ that (1) has an intuitive interpretation as an action forming combinator and (2) does not impose restrictions on the use of other relevant action combinators such as sequence and iteration, and (3) has a meaningful interpretation in the normative context. The second problem we address concerns the reduction from deontic assertions to dynamic logic assertions. Our first point is that we want this reduction to obey the free-choice semantics for norms. For ought-to-be deontic logics it is generally accepted that the free-choice semantics is counter-intuitive. But for dynamic deontic logics we actually consider it a viable, if not, the better alternative. Our second concern with the reduction is that we want it to be more liberal than the ones that were proposed before in the literature. For instance, Meyer's reduction does not leave room for action whose normative status is neither permitted nor forbidden. We test the logics we define in this paper against a set of minimal logic requirements.     

Anti-intuitionism and paraconsistency

This paper aims to help to elucidate some questions on the duality between the intuitionistic and the paraconsistent paradigms of thought, proposing some new classes of anti-intuitionistic propositional logics and investigating their relationships with the original intuitionistic logics. It is shown here that anti-intuitionistic logics are paraconsistent, and in particular we develop a first anti-intuitionistic hierarchy starting with Johansson's dual calculus and ending up with Gödel's three-valued dual calculus, showing that no calculus of this hierarchy allows the introduction of an internal implication symbol. Comparing these anti-intuitionistic logics with well-known paraconsistent calculi, we prove that they do not coincide with any of these. On the other hand, by dualizing the hierarchy of the paracomplete (or maximal weakly intuitionistic) many-valued logics (Iⁿ)_nω we show that the anti-intuitionistic hierarchy (I^n*)_nω obtained from (Iⁿ)_nω does coincide with the hierarchy of the many-valued paraconsistent logics (Pⁿ)_nω. Fundamental properties of our method are investigated, and we also discuss some questions on the duality between the intuitionistic and the paraconsistent paradigms, including the problem of self-duality. We argue that questions of duality quite naturally require refutative systems (which we call elenctic systems) as well as the usual demonstrative systems (which we call deictic systems), and multiple-conclusion logics are used as an appropriate environment to deal with them.     

Logics of public communications

Multi-modal versions of propositional logics S5 or S4—commonly accepted as logics of knowledge—are capable of describing static states of knowledge but they do not reflect how the knowledge changes after communications among agents. In the present paper (part of broader research on logics of knowledge and communications) we define extensions of the logic S5 which can deal with public communications. The logics have natural semantics. We prove some completeness, decidability and interpretability results and formulate a general method that solves certain kind of problems involving public communications—among them well known puzzles of Muddy Children and Mr. Sum & Mr. Product. As the paper gives a formal logical treatment of the operation of restriction of the universe of a Kripke model, it contributes also to investigations of semantics for modal logics. This paper was originally published as Plaza, J. A. (1989). Logics of public communications. In M. L. Emrich, M. S. Pfeifer, M. Hadzikadic, & Z.W. Ras (Eds.), Proceedings of the fourth international symposium on methodologies for intelligent systems: Poster session program (pp. 201–216). Publisher: Oak Ridge National Laboratory, ORNL/DSRD-24. Research partly supported by NSF Grant CCR-8702307 and PSC-CUNY Grant 668283.     

The Port-Royal semantics of terms

Conclusion It is tempting to say from the contemporary point of view that thePort-Royal Logic is full of confusions as well as insights. I have focused on several of these confusions and their relations, in particular the confusions between complex idea and proposition, between proposition and judgment, and especially between name and predicate. In particular I have tried to emphasize the instability of the Port-Royal semantics — the ways in which their theory of terms vacillates between earlier views and something closer to a modern analysis. It may, however, be more profitable to regard this work as incorporating several logics, and to view the confusions as the inevitable results of the dynamical tensions among these different views.     

Structural representation and surrogative reasoning

It is argued that a number of important, and seemingly disparate, types of representation are species of a single relation, here called structural representation, that can be described in detail and studied in a way that is of considerable philosophical interest. A structural representation depends on the existence of a common structure between a representation and that which it represents, and it is important because it allows us to reason directly about the representation in order to draw conclusions about the phenomenon that it depicts. The present goal is to give a general and precise account of structural representation, then to use that account to illuminate several problems of current philosophical interest — including some that do not initially seem to involve representation at all. In particular, it is argued that ontological reductions (like that of the natural numbers to sets), compositional accounts of semantics, several important sorts of mental representation, and (perhaps) possible worlds semantics for intensional logics are all species of structural representation and are fruitfully studied in the framework developed here.     

Comparing Semantics of Logics for Multi-Agent Systems

We draw parallels between several closely related logics that combine — in different proportions — elements of game theory, computation tree logics, and epistemic logics to reason about agents and their abilities. These are: the coalition game logics CL and ECL introduced by Pauly 2000, the alternating-time temporal logic ATL developed by Alur, Henzinger and Kupferman between 1997 and 2002, and the alternating-time temporal epistemic logic ATEL by van der Hoek and Wooldridge (2002). In particular, we establish some subsumption and equivalence results for their semantics, as well as interpretation of the alternating-time temporal epistemic logic into ATL. The focus in this paper is on models: alternating transition systems, multi-player game models (alias concurrent game structures) and coalition effectivity models turn out to be intimately related, while alternating epistemic transition systems share much of their philosophical and formal apparatus. Our approach is constructive: we present ways to transform between different types of models and languages.     

All Finitely Axiomatizable Tense Logics of Linear Time Flows Are CoNP-complete

We prove that all finitely axiomatizable tense logics with temporal operators for ‘always in the future’ and ‘always in the past’ and determined by linear fows time are coNP-complete. It follows, for example, that all tense logics containing a density axiom of the form ■ⁿ⁺¹_F p → ⁿ_F p, for some n ≥ 0, are coNP-complete. Additionally, we prove coNP-completeness of all ∩-irreducible tense logics. As these classes of tense logics contain many Kripke incomplete bimodal logics, we obtain many natural examples of Kripke incomplete normal bimodal logics which are nevertheless coNP-complete.     

The False Consensus Effect and Overconfidence: Flaws in Judgment or Flaws in How We Study Judgment?

Thefalse consensus effectand theoverconfidence in judgmenteffect are often referred to as established “facts” of psychology. At present, the empirical support for these effects is inadequate and logically flawed. We argue that, absent other information, using one's own response to a situation as an observation of size 1 could be an effective use of data and could lead to anincreasein the accuracy of predicting others’ behavior. In an empirical examination of such use, we find a robustpositivecorrelation between the degree to which people believe that a majority of others are like them and their accuracy in predicting those others’ responses, whether this correlation is evaluated within items across people, across items within people, or across items across people. In addition, we show that the finding of overconfidence in judgment follows analytically from the functional relationship used to demonstrate it, a “finding” that is easily reversed by considering the inverse relationship. Specifically, we argue that regression effects account for the evidence cited in support of overconfidence. While not definitive, our empirical findings call into the question the acceptance of these two effects—as commonly defined—as facts.     

Semantics for Dual and Symmetric Combinatory Calculi

We define dual and symmetric combinatory calculi (inequational and equational ones), and prove their consistency. Then, we introduce algebraic and set theoretical– relational and operational – semantics, and prove soundness and completeness. We analyze the relationship between these logics, and argue that inequational dual logics are the best suited to model computation.     

Attention to faces modulates early face processing during low but not high face discriminability

In the present study, we investigated whether attention to faces results in sensory gain modulation. Participants were cued to attend either to faces or to scenes in superimposed face—scene images for which face discriminability was manipulated parametrically. The face-sensitive N170 event-related potential component was used as a measure of early face processing. Attention to faces modulated N170 amplitude, but only when faces were not highly discriminable. Additionally, directing attention to faces modulated later processing (~230—300 msec) for all discriminability levels. These results demonstrate that attention to faces can modulate perceptual processing of faces at multiple stages of processing, including early sensory levels. Critically, the early attentional benefit is present only when the “face signal” (i.e., the perceptual quality of the face) in the environment is suboptimal.     

Filter distributive logics

The present paper is thought as a formal study of distributive closure systems which arise in the domain of sentential logics. Special stress is laid on the notion of a C-filter, playing the role analogous to that of a congruence in universal algebra. A sentential logic C is called filter distributive if the lattice of C-filters in every algebra similar to the language of C is distributive. Theorem IV.2 in Section IV gives a method of axiomatization of those filter distributive logics for which the class Matr (C) _prime of C-prime matrices (models) is axiomatizable. In Section V, the attention is focused on axiomatic strengthenings of filter distributive logics. The theorems placed there may be regarded, to some extent, as the matrix counterparts of Baker's well-known theorem from universal algebra [9, § 62, Theorem 2].The contents of this paper were presented in a talk at the 7th International Congress of Logic, Methodology and Philosophy of Science held at Salzburg, Austria, in July 1983. In abstracted form the paper was published in Abstracts of the 7th Congress, Vol. 2, pp. 39– 42. We take this opportunity to thank Professor Paul Weingartner and Doctor Georg Dorn from Salzburg for their (not fulfilled) wish to publish the present version in a special volume containing a selection of contributions to the 7th Congress.