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LINGUISTIX&LOGIK, Tony Marmo's blog
Monday, 18 July 2005

Topic: Interconnections

The Gamut of Dynamic Logics

By Jan van Eijck & Martin Stokhof

Dynamic logic, broadly conceived, is the logic that analyses change by decomposing actions into their basic building blocks and by describing the results of performing actions in given states of the world. The actions studied by dynamic logic can be of various kinds: actions on the memory state of a computer, actions of a moving robot in a closed world, interactions between cognitive agents performing given communication protocols, actions that change the common ground between speaker and hearer in a conversation, actions that change the contextually available referents in a conversation, and so on.
In each of these application areas, dynamic logics can be used to model the states involved and the transitions that occur between them. Dynamic logic is a tool for both state description and action description. Formulae describe states, while actions or programs express state change. The levels of state descriptions and transition characterisations are connected by suitable operations that allow reasoning about pre- and post-conditions of particular changes.
From a computer science perspective, dynamic logic is a formal tool for reasoning about programs. Dynamic logics provides the means for formalising correctness specifications, for proving that these speci cations are met by a program under consideration, and for reasoning about equivalence of programs. From the perspective of the present paper, this is but one of many application areas. We will also look at dynamic logics for cognitive processing, for communication and information updating, and for various aspects of natural language understanding.

Source: Online Papers in Philosophy

Posted by Tony Marmo at 23:51 BST
Friday, 8 July 2005

Topic: Interconnections

Definability and Invariance

By Newton C. A. da Costa & Alexandre Augusto Martins Rodrigues

In his thesis Para uma Teoria Geral dos Homomorfismos (1944), the Portuguese mathematician José Sebastião e Silva constructed an abstract or generalized Galois theory, that is intimately linked to F. Klein's Erlangen Program and that foreshadows some notions and results of today's model theory; an analogous theory was independently worked out by M. Krasner in 1938. But Silva's work on the subject is neither wholly clear nor sufficiently rigorous. In this paper we present a rigorous version of the theory, correcting the shortcomings of Silva's exposition and extending some of its main results.

Source: CLE
Of related interest: Remarks on Abstract Galois Theory by Newton C.A. da Costa.

Posted by Tony Marmo at 02:41 BST
Updated: Friday, 8 July 2005 02:48 BST


Posted by Tony Marmo at 02:26 BST


Dialectical Considerations on the Logic of Contradiction: Part I

By John Woods

This is an examination of the dialectical structure of deep disagreements about matters not open to empirical check. A dramatic case in point is the Law of Non-Contradiction (LNC). Dialetheists are notoriously of the view that, in some few cases, LNC has a true negation. The traditional position on LNC is that it is non-negotiable. The standard reason for thinking it non-negotiable is, being a first principle, there is nothing to negotiate. One of my purposes is to show that the first-principle defence of LNC is inadequate. A second purpose is to argue that it flows from this inadequacy that LNC stands or falls on economic considerations, much in the spirit of Quine's pragmatism about logic generally. This is a tactical victory for dialetheists. It gives them room to make the case against LNC on cost-benefit grounds. As things presently stand, no such case can be considered decisive. But, given that costs and benefits shift with changing circumstances, it is possible that a winning case for the dialetheist may present itself in the future. Notwithstanding the rivalry between consistentists and dialetheists, they share a common opponent. This is trivialism, the doctrine that everything whatever is true. It is an ironic alliance, in as much as the dialetheist's case against the consistentist can be adapted to a defence of trivialism. How damaging this turns out to be depends on the adequacy of the reasons for the dialetheist's rejection of trivialism. My further purpose is to show that the damage is slighter than dialetheists commonly believe.

Key Words: antinomy, Aristotle, contradiction, costs and benefits, consistentism, Curry Paradox, detonation, dialetheism, Frege, Law of Non-Contradiction, Liar Paradox, Locke, proof, Russell, near-trivialism, paraconsistency, Philosophy's Most Difficult Problem, set theory, semantics, Solving Paradox, Tarski, truth

Appeared in the Logic Journal of IGPL 2005 13(2):231-260

Posted by Tony Marmo at 00:01 BST
Updated: Friday, 8 July 2005 02:20 BST


Modality and Paraconsistency

By João Marcos

Paraconsistent logic was born in the vicinity of modal logic. Moreover, as every other non-classical logicians, paraconsistentists have very often flirted with modalities. The first known system of paraconsistent logic was in fact defined as a fragment of S5, in the late 40s. But a fragment of a modal system is not necessarily a modal system. I will show here, indeed, that Jaškowski’s D2 is not a modal logic, in the contemporary usual meaning of the term. By contrast, I will also show, subsequently, that any non-degenerate normal modal system is inherently paraconsistent.

Appeared in
[i.] Marta Bilkova and Libor Behounek (eds), The Logica Yearbook 2004, Filosofia, Prague, 2005, pp.213-222.
[ii.] Marcos (2005), Logics of Formal Inconsistency, Chapter 3.2, pp. 211-219. Unicamp press.

Posted by Tony Marmo at 00:01 BST
Updated: Friday, 8 July 2005 02:21 BST


Logics of essence and accident

By João Marcos

We say that things happen accidentally when they do indeed happen, but only by chance. In the opposite situation, an essential happening is inescapable, its inevitability being the sine qua non for its very occurrence. This paper will investigate modal logics on a language tailored to talk about essential and accidental statements. Completeness of some among the weakest and the strongest such systems is attained. The weak expressibility of the classical propositional language enriched with the non-normal modal operators of essence and accident is highlighted and illustrated, both with respect to the definability of the more usual modal operators as well as with respect to the characterizability of classes of frames. Several interesting problems and directions are left open for exploration.

Keywords: philosophy of modal logic, non-normal modalities, formal metaphysics, essence, accident

Appeared in
[i.] Bulletin of the Section of Logic, 34(1):43-56, 2005
[ii.] Marcos (2005) Logics of Formal Inconsitency, Chapter 3.1: 199-210

Sources: João Marcos' Webpage, Paraconsistency group, Paraconsistent Newsletter.

Posted by Tony Marmo at 00:01 BST
Updated: Friday, 8 July 2005 02:19 BST


A Paraconsistent -preservationist approach to a common confusion concerning predicate-extensions

By Martin W. Allen

The existence of multiple criteria for the introduction of a predicate may lead to confusion when the criteria diverge as to whether or not some object falls under the predicate. It can be dicult to represent the semantics of sentences featuring such a predicate-term, and it is not obvious how a person is supposed to employ such confused terms in the business of language and reasoning. I consider [here] two approaches to the problem: dialethism, which allows both a sentence and its negation to be true at once; and disambiguation, which represents any such confused predicate in terms of other ,distinct predicates. I show the equivalency of plausible formal treatments of these approaches, discuss reasons for this equivalency, and present an alternative approach|a preservationist one, which does not interpret the confused predicates but rather seeks to contain the confusion present. I argue that a meaningful, and useful, concept of inference is available, even where the semantics of certain predicate-terms remain confusing.

Posted by Tony Marmo at 00:01 BST
Updated: Friday, 8 July 2005 02:19 BST
Thursday, 7 July 2005

Now Playing: UPDATED
Update: Today I received Jo?o Marcos' book, Logics of Formal Inconsistency.Thanks Jo?o!!

Paraconsistency For Beginners

Joao Marcos' book has an important section for beginners. From page 16 to page 30, Chapter 1.0 (it would be Chapter 2 or an appendix to Chapter 1, but Jo?o liked the idea of calling it 1.0), there is a very easy exposition of what is Paraconsistent Logic. Section 2 of the same Chapter requires more attention from the reader, but by reading the first Section one is relatively prepared to understand Section 2, which is not very difficult.
So, teachers, here is my recommendation: Joao Marcos? Chapter 1.0 for your undergraduates.

February the 17th 2005

Yesterday, Joao Marcos defended his PhD dissertation, as the Unicamp Portal infoms us. Here is an abstract with a link:

Logics of Formal Inconsistency

By Joao Marcos

According to the classical consistency presupposition, contradictions have an explosive character: Whenever they are present in a theory, anything goes, and no sensible reasoning can thus take place. A logic is paraconsistent if it disallows such presupposition, and allows instead for some inconsistent yet non-trivial theories to make perfect sense. The Logics of Formal Inconsistency, LFIs, form a particularly expressive class of paraconsistent logics in which the metatheoretical notion of consistency can be internalized at the object-language level. As a consequence, the LFIs are able to recapture consistent reasoning by the addition of appropriate consistency assumptions. So, for instance, while classical rules such as disjunctive syllogism (from A and not-A-or-B, infer B) are bound to fail in a paraconsistent logic (because A and not-A could both be true for some A, independently of B), they can be recovered by an LFI if the set of premises is enlarged by the presumption that we are reasoning in a consistent environment (in this case, by the addition of consistent-A as an extra hypothesis of the rule).
The present monograph introduces the LFIs and provides several illustrations of them and of their properties, showing that such logics constitute in fact the majority of interesting paraconsistent systems from the literature. Several ways of performing the recapture of consistent reasoning inside such inconsistent systems are also illustrated. In each case, interpretations in terms of many-valued, possible-translations, or modal semantics are provided, and the problems related to providing algebraic counterparts to such logics are surveyed. A formal abstract approach is proposed to all related definitions and an extended investigation is made into the logical principles and the positive and negative properties of negation.

Keywords: Universal Logic, negation, paraconsistency, possible-translations semantics, modalities, formal philosophy.

PhD Dissertation, Cooperation Agreement between the State University of Campinas and the Technical University of Lisbon

Note: As the members of the Commission have offered Jo?o Marcos many suggestions, it is possible that a new revised text will appear sooner or later, though most of the Chapters have been already published as separate papers in different journals.

Posted by Tony Marmo at 00:01 BST
Updated: Friday, 8 July 2005 02:24 BST
Monday, 4 July 2005

Topic: Interconnections

The Elimination of Self-Reference
(Generalized Yablo-Series and the Theory of Truth)

By Phillippe Schlenker

Although it was traditionally thought that self-reference is a crucial ingredient of semantic paradoxes, Yablo showed that this is not so by displaying an infinite series of non-referential sentences which, taken together, are paradoxical (e.g. Yablo 2004). We generalize Yablo's result along two dimensions.
1. First, we investigate the behavior of Yablo-style series of the form {<s(i), [Qk: k> i] f[(s(k)) k≥i ]>: i≥0}, where for each i s( i) is a term that denotes the sentence [Qk: k> i] f[(s(k)) k≥i] ] (for some generalized quantifier Q and for some (fixed) truth function f). We show that for any n-valued compositional semantics and for any quantifier Q that satisfies certain natural properties, all the sentences in the series must have the same value. We derive a characterization of those values of Q for which the series is paradoxical in a natural trivalent logic.
2. Second, we show that in the Strong Kleene trivalent logic, Yablo's results are a special case of a much more general phenomenon: given certain assumptions, any semantic phenomenon that involves self-reference can be reproduced without self-reference (Cook 2004 proves a special case of this result, which only applies to logical paradoxes).

Specifically, we can associate to each pair <s, F> of a formula F named by a term s in a language L' a series of translations {<s( i), [Qk: k> i] [F] k>: i≥0} (where [F] kis a certain modification of F) in a quantificational language L* in such a way that
(i) none of the translations are self-referential,
(ii) in any fixed point I* of L*, all the translations of a given formula of L have the same value according to I*, and
(iii) there is a correspondence between the fixed points of L' and the fixed points of L* which ensures that the translations really do have the same semantic behavior as the sentences they translate.

We give a characterization of those generalized quantifiers Q which can be used in the translation.
Source: Online Papers in Philosophy

Posted by Tony Marmo at 07:15 BST
Updated: Monday, 4 July 2005 07:24 BST
Saturday, 2 July 2005

Topic: Cognition & Epistemology

Reference Determination and Conceptual Change

By Ingo Brigandt

The paper discusses reference determination from the point of view of conceptual change in science. The first part of the discussion uses the homology concept, a natural kind term from biology, as an example. It is argued that the causal theory of reference gives an incomplete account of reference determination even in the case of natural kind terms. Moreover, even if descriptions of the referent are taken into account, this does not yield a satisfactory account of reference in the case of the homology concept. I suggest that in addition to the factors that standard theories of reference invoke the scientific use of concepts and the epistemic interests pursued with concepts are important factors in determining the reference of scientific concepts. In the second part, I argue for a moderate holism about reference determination according to which the set of conditions that determine the reference of a concept is relatively open and different conditions may be reference fixing depending on the context in which this concept is used. It is also suggested that which features are reference determining in a particular case may depend on the philosophical interests that underlie reference ascription and the study of conceptual change.

Source: Online Papers in Philosophy

Posted by Tony Marmo at 07:20 BST
Tuesday, 28 June 2005


On the Lumping Semantics of Counterfactuals

By Makoto Kanazawa, Stefan Kaufmann and Stanley Peters

Kratzer (1981) discussed a naïve premise semantics of counterfactual conditionals, pointed to an empirical inadequacy of this interpretation, and presented a modification— partition semantics— which Lewis (1981) proved equivalent to Pollock's (1976) version of his ordering semantics. Subsequently, Kratzer (1989) proposed lumping semantics, a different modification of premise semantics, and argued it remedies empirical failings of ordering semantics as well as of naïve premise semantics. We show that lumping semantics yields truth conditions for counterfactuals that are not only different from what she claims they are, but also inferior to those of the earlier versions of premise semantics.

See also the Journal of Semantics 2005 22(2):129-151

Constraining Premise Sets for Counterfactuals

By Angelika Kratzer

This note is a reply to "On the Lumping Semantics of Counterfactuals" by Makoto Kanazawa, Stefan Kaufmann, and Stanley Peters. It argues first that the first triviality result obtained by Kanazawa, Kaufmann, and Peters does not apply to the analysis of counterfactuals in Kratzer (1989). Second, and more importantly, it points out that the results obtained by Kanazawa, Kaufmann, and Peters are obsolete in view of the revised analysis of counterfactuals in Kratzer (1990, 2002).

Posted by Tony Marmo at 00:01 BST
Updated: Tuesday, 28 June 2005 08:39 BST
Friday, 24 June 2005


On the practice of indirect reports

by Alessandro Capone

In this paper, I shall deal with the practice of indirect speech reports. I shall argue that indirect speech reports are transformations of original speech events (or speech acts), subject to severe limitations, which it is my aim in this paper to spell out in detail. I shall study the interactions with the theory of pragmemes, of indexicals, and of modes of presentation. I end this paper suggesting, given appropriate evidence, that a key to the understanding of indirect reports is the exploration of analogies with the theory of speech acts and that analogies with the theory of propositional attitudes may be misleading.

Source: Semantics Archive

Posted by Tony Marmo at 23:19 BST
Wednesday, 22 June 2005


On the Storeyed Revenge of Strengthened Liars

By Jordan Howard Sobel

The Strengthened Liar observes that if we follow a partiality theorist and declare the Liar sentence neither true nor false (or failing to express a proposition, or suffering from some sort of grave semantic defect), then the paradox is only pushed back. For we can go on to conclude that whatever this status may be, it implies that the Liar sentence is not true. This claim is true, but it is just the Liar sentence again. We are back in paradox. (Glanzberg 2002, p. 468; 2004, p. 29; 2001, p. 222, “We are back in our contradiction.”)

There are problems with this charge that strengthened liar sentences avenge would be disparagements that they do not express propositions, by reappearing as claims that are easy consequences of these disparagements. For one thing, if, as one supposes, claims would be propositions not sentences, [t]his claim cannot be the Liar sentence again. (Cf., Grim 1991, p. 19.) For another thing, while it does follow from the disparagement that a Liar sentence does not express a proposition, that this sentence does not express a true proposition, it is a consequence of that disparagement that this claim or proposition is not expressed by the Liar sentence itself. However, there are ways in which informal and formal revelations that Liar sentences do not express propositions and seem to bring them back with vengeance. This is their story.

Source: Online Papers in Philosophy

Posted by Tony Marmo at 03:55 BST
Updated: Wednesday, 22 June 2005 04:03 BST
Tuesday, 21 June 2005


Standard and Non-Standard Quantifiers in Natural Language

By Edward L. Keenan

Since the early 1980s we have been witnessing an explosive growth in our knowledge of natural language quantifiers, specifically of their denotations as opposed to their form, distribution, or compositional interpretation. Our concern here is to unify and extend these results, highlighting generalizations of linguistic interest. We present first an inventory of semantically defined classes of quantifiers expressible in English, and then a list of linguistic generalizations stated in terms of these classes and their defining concepts. We close with two types of quantification that lie outside these classes and which invite further research as less is known about them.

Source: Online Papers in Philosophy

Posted by Tony Marmo at 03:03 BST
Thursday, 16 June 2005


Zero Tolerance for Pragmatics

By Christopher Gauker

The proposition expressed by a sentence is relative to a context. But what are the values of the context variables? Many theorists would include among these values aspects of the speaker's intention in speaking. My thesis is that, on the contrary, the values of the context variables never include the speaker's intention. My argument for this thesis turns on a consideration of the role that the concept of proposition expressed in context is supposed to play in a theory of linguistic communication and on a consideration of what a speaker and a hearer can reasonably expect of one another. Although I call this thesis zero tolerance for pragmatics, it is not an expression of intolerance for everything that might be called pragmatics.

Source: Online Papers in Philosophy

Posted by Tony Marmo at 07:48 BST
Updated: Thursday, 16 June 2005 07:59 BST

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