The home page for the philosophy of paraconsistency

Aim of this site

This site results, among others, from discussions between Jean-Yves Beziau and Alessio Moretti, about the philosophical relevance of paraconsistent logic. It's aim is to offer a frame to all searchers interested in exploring the philosophical implications of the many logical systems and approaches going under the general banner "paraconsistency". The analysis is, more or less, the following :

1) paraconsistent logic is by now a quite well established branch of mathematics, exploring mainly the properties of logical "negation". One has to note that the many technical results about paraconsistency are still quite unknown to the non-paraconsistent working mathematician, not to speak about the philosopher not used to mathematical formalisms.
2) Although paraconsistency was, at his beginning, motivated by deep philosophical reasons, it seems, by some kind of paradox, that now that the technical machinery has reached a satisfactory level of maturity, the philosophical interpretations of this new logical landscape are very few and still seem to lack of philosophical depth, at least in the sense of not (yet) reaching the scope of possible applications.
3) This unsatisfactory situation of the philosophical side of the enterprise is not due to some intrinsic reason of the subject, say "paraconsistency is not philosophically interesting". On the contrary, paraconsistency is highly interesting, probably crucial, to the philosopher (i.e. to all kinds of philosophers), and the relative poverty of the reflection thereupon is more a matter of coordination of the researchers and of accessibility, for the professional philosopher, of the technical discoveries, these being most of the time rather unintelligible to that respectable majority of philosophers not that much used to mathematical sophistication.
4) Which gives us the policy to follow for our present project : <...>

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Posted by Tony Marmo at 01:01 BST

Updated: Monday, 30 August 2004 02:02 BST

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An Expressive First-Order Logic with Flexible Typing for Natural Language Semantics

by Chris Fox and Shalom Lappin

We present Property Theory with Curry Typing (PTCT), an intensional first-order logic for natural language semantics. PTCT permits fine-grained specifications of meaning. It also supports polymorphic types and separation types. 1We develop an intensional number theory within PTCT in order to represent proportional generalized quantifiers like most . We use the type system and our treatment of generalized quantifiers in natural language to construct a type-theoretic approach to pronominal anaphora that avoids some of the difficulties that undermine previous type-theoretic analyses of this phenomenon.

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Posted by Tony Marmo at 09:07 BST

Updated: Wednesday, 25 August 2004 09:34 BST

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Hempel's Raven Paradox: A Lacuna in the Standard Bayesian Solution

by Peter B. M. Vranas

According to Hempel's paradox, evidence (E) that an object is a nonblack nonraven confirms the hypothesis (H) that every raven is black. According to the standard Bayesian solution, E does confirm H but only to a minute degree. This solution relies on the almost never explicitly defended assumption that the probability of H should not be affected by evidence that an object is nonblack. I argue that this assumption is implausible, and I propose a way out for Bayesians.

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Posted by Tony Marmo at 03:14 BST

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The Fuzzy Logic Debate [1]

Fuzzy Logic: Misconceptions and Clarifications

by Carl W. Entemann

Some commonly accepted statements concerning the basic fuzzy logic proposed by Lotfi Zadeh in 1965, have led to suggestions that fuzzy logic is not a logic in the same sense as classical bivalent logic. Those considered herein are: fuzzy logic generates results that contradict classical logic, fuzzy logic collapses to classical logic, there can be no proof theory for fuzzy logic, fuzzy logic is inconsistent, fuzzy logic produces results that no human can accept, fuzzy logic is not proof-theoretic complete, fuzzy logic is too complex for practical use, and, finally, fuzzy logic is not needed. It is either proved or argued herein that all of the these statements are false and are, hence, misconceptions. A fuzzy logic with truth values specified as subintervals of the real unit interval [0.0, 1.0] is introduced. Proofs of the correctness, consistency, and proof theoretic completeness of the truth interval fuzzy logic are either summarized or cited. It is concluded that fuzzy logics deserve the accolade of logic to the same degree that the term applies to classical logics.

Keywords:
knowledge management, logic inference, logic processing, theorem proving, uncertainty, uncertainty reasoning
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The Fuzzy Logic Debate [2]

On Some Alleged Misconceptions about Fuzzy Logic

by Francis Jeffry Pelletier


Entemann (2002) defends fuzzy logic by pointing to what he calls `misconceptions' concerning fuzzy logic. However, some of these `misconceptions' are in fact truths, and it is Entemann who has the misconceptions. The present article points to mistakes made by Entemann in three different areas. It closes with a discussion of what sort of general considerations it would take to motivate fuzzy logic.


Keywords:
Fuzzy Logic, Proof Theory, Truth Interval Tableaux
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Posted by Tony Marmo at 05:44 BST

Updated: Monday, 23 August 2004 05:58 BST

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Natural Language Semantics' TOP 3

Focus Below the Word Level
by Ron Artstein
The Interpretation of Traces
by Uli Sauerland
Crossover Situations
by Daniel Buring

Posted by Tony Marmo at 05:20 BST

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A Poor Concept Script

by Hartley Slater
Source: AJL


The formal structure of Frege's `concept script' has been widely adopted in logic text books since his time, even though its rather elaborate symbols have been abandoned for more convenient ones. But there are major difficulties with its formalisation of pronouns, predicates, and propositions, which infect the whole of the tradition which has followed Frege. It is shown first in this paper that these difficulties are what has led to many of the most notable paradoxes associated with this tradition; the paper then goes on to indicate the lines on which formal logic--and also the lambda calculus and set theory--needs to be restructured, to remove the difficulties.

Throughout the study of what have come to be known as first-, second-, and higher-order languages, what has been primarily overlooked is that these languages are abstractions. Many well known paradoxes, we shall see, arose because of the elementary level of simplification which has been involved in the abstract languages studied. Straightforward resolutions of the paradoxes immediately appear merely through attention to languages of greater sophistication, notably natural language, of course. The basic problem has been exclusive attention to a theory in place of what it is a theory of, leading to a focus on mathematical manipulation, which `brackets off' any natural language reading.

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Posted by Tony Marmo at 01:01 BST

Updated: Sunday, 22 August 2004 01:03 BST

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Information State Update: Semantics or Pragmatics?

by Raquel Fern?ndez and Matthew Purver (2004)

We argue for an approach which treats the compositional semantic content of an utterance as including its basic dialogue update effects - those which can be derived entirely from its semantic and syntactic properties.

This allows us to capture the distinction between these integral semantic contextual effects and those pragmatic effects which can only be determined from the interaction between features of the utterance and the context itself.

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Posted by Tony Marmo at 18:22 BST

Updated: Friday, 20 August 2004 18:24 BST

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The summer is nearing its end. I just finished the first draft syllabus for my pragmatics course this fall. I hope to condense some of the introduction to basic concepts, primarily by reigning in my tendency to get caught up in digressions. This will give me time to cover some interesting topics under current investigation, which I am quite excited about. We'll see how it goes.

This is a dress rehearsal of sorts for the 6 week pragmatics course that I will be teaching during the LSA Summer Linguistics Institute 2005 next summer. I will only have twelve 90 minute sessions, so that version will have to be even more concentrated.

Source: Semantics-etc

Posted by Tony Marmo at 05:45 BST

Updated: Friday, 20 August 2004 05:53 BST

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Semantics in Context

by Jason Stanley
Source: lingBuzz/000024

(...)The explanation for our ability to report about the truth and falsity of what is said by an utterance of

Some philosophers are from New York

in various possible situations is as follows. Competent English speakers know the meanings of the words used, and understand how they are combined. Their grasp of the truth-conditions of the utterance of that sentence is due to their ability to combine the meanings of the words, relative to the context of utterance.
With this explanation in mind, consider an utterance of the sentence

Every philosopher is from New York,

made at a small philosophy conference. It is natural to take this utterance to say something that is true if and only if every philosopher at the conference is from New York. If we cleave to the model of understanding just described, we will seek to explain our understanding of the truth-conditions of this utterance by appeal to a process of combining the elements of the sentence "Every philosopher is from New York", using our understanding of the words used in the sentence. But of course, there appears to be no expression in the sentence "Every philosopher is from New York" that corresponds to the understood constituent expressed by "at this conference".
Similarly, suppose, pointing at a 5 foot tall seven year old child, I utter the sentence "He is tall." I am most naturally understood as saying something that is true if and only if the child in question is tall for a seven year old child. Preserving the model of understanding we began with, according to which our intuitions about the truth-conditions of an utterance are due to a process of combining meanings of the parts of the sentence uttered, would require us to find some constituent in the sentence that could be taken to supply the understood property of being a seven year old child. But again, it appears that the sentence "He is tall" contains no such constituent. So, we have a predicament. If we look at certain sentences, there seems to be a clear and elegant explanation of why we have the intuitions we do about the truth conditions of utterances of those sentences. But if we consider utterances of other sentences, the explanation appears to break down. The first response to this predicament is to attempt to preserve the clear and elegant explanation in the face of the apparently recalcitrant data. The second is to abandon the clear and elegant explanation of the source of our truth-conditional intuitions in favor of a different one.
My concern with the second response to the predicament is that the suggestions I am aware of for dealing with the additional complexity essentially end up abandoning the project of giving a systematic explanation of the source of our intuitions. They invariably involve appeal to unconstrained and non-explanatory notions or processes (cf. Stanley (2002a)). I have therefore been inclined to pursue the first of these options (cf. Stanley (2000)). My purpose in this paper is to continue the project of defending the clear and elegant explanation of the source of our intuitions about the truth-conditions of utterances. I will do so by considering some replies to previous arguments in favor of it. I will argue that proponents of abandoning the clear and elegant explanation have not yet made their case.
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Posted by Tony Marmo at 19:31 BST

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The aspectual impact of French locative goal PPs

by Olivier Bonami

This paper presents an attempt to account for the aspectual class alternations induced by locative goal PPs in combination with motion verbs. It is noted that in French, two semantically distinct classes of prepositions (e.g. dans vs. jusqu'a ) give rise to telic eventuality descriptions in combination with basically atelic motion verbs. Moreover, the resulting sentences exhibit differing and peculiar aspectual properties. Thus the conventional analysis, which states that the PP provides a spatio-temporal boundary to the event described by the verb is at least insufficient.

The proposed analysis rests on the idea that goal PPs function as co-predicators (Gawron 1986). Sentences containing goal PPs are composite eventuality descriptions, the verb and the preposition describing different parts of a structured event. The peculiar aspectual properties of sentences containing goal PPs is related to their composite nature. A situation-theoretic formalization is proposed, which allows to view the aspectual impact of the goal PPs as a side effect of co-predication.

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Posted by Tony Marmo at 01:01 BST

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Prepositional Aspect and the Algebra of Paths

by Joost Zwarts

The semantics of directional prepositions is investigated from the perspective of aspect. What distinguishes telic PPs (like to the house) from atelic PPs (like towards the house), taken as denoting sets of paths, is their algebraic structure:
atelic PPs are cumulative, closed under the operation of concatenation,
telic PPs are not.
Not only does this allow for a natural and compositional account of how
PPs contribute to the aspect of a sentence, but it also guides our understanding of the lexical semantics of prepositions in important ways. Semantically, prepositions turn out to be quite similar to nouns and verbs. Nominal distinctions (like singular and plural, mass and count) and verbal classes (like semelfactives and degree achievements) have their prepositional counterparts.

Source: Semantic Archive

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Posted by Tony Marmo at 20:01 BST

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On resumptive relatives and the theory of LF chains

by Valentina Bianchi

In various languages, resumptive relativization is a normal strategy alongside "gap" relativization. Recent research on resumptive relatives has concentrated mainly on the distribution of resumptive pronouns along the "NP Accessibility Hierarchy" proposed by Keenan & Comrie (1977). It has been pointed out that cross-linguistically, gap relativization tends to occur in the highest positions of the NP-accessibility hierarchy, whereas resumptive pronouns tend to be obligatory in the lower oblique positions (see Su??er 1998 for a recent general overview).
There are, however, some languages in which the two strategies seem to freely alternate at least in the direct object position. In this paper I will argue that the alternation between a gap and a resumptive pronoun is sensitive to a special factor, namely, the type of the relative clauses. I will adopt the three-way typology proposed by Grosu & Landman (1996), which distinguishes non-restrictive, restrictive, and "maximalizing" relatives. On the basis of this typology, I will propose an empirical generalization on the distribution of resumptive pronouns and I will try to derive it from an elaboration of Rizzi's (1997) theory of LF chains.

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Posted by Tony Marmo at 06:13 BST

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Pseudo Weak Crossover in French relative clauses &
global economy

byBenjamin Spector

(1) Le/( ?)Aucun type que(1) son(1) p?re a frapp? t(1) a pleur?.

The/ No guy that(1) his(1) father has beaten t(1) has cried.

(2) *Le/*Aucun type dont(1) le p?re t(1) l(1)' a frapp? a pleur?.

The/No guy of-whom(1) the father t(1) him(1) has beaten has cried.

Both (1) and (2) are WCO violations, since in both cases the trace does not c-command the pronoun; yet (1) is fine but (2) isn't. Note that (2) would be acceptable with another co-indexing.

(...)The hypothesis I will defend in this paper is similar in spirit to a proposal put forward in Ruys (1994): among the structures that could realize the logical form in question, the most economic one, in a sense to be defined, is preferred. More precisely, grammar generates a set of structures corresponding to a given logical form; a metric is defined over these structures, and the most economic structure is preferred to all others. A crucial point here is that this comparison process will apply only to structures that are otherwise wellformed, i.e. which, for instance, do not violate any known locality constraint. An immediate prediction that is made is that when one of the two potential candidates cannot be generated by the grammar, then there will be only one candidate, which will therefore be selected as the most economic one.

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Posted by Tony Marmo at 01:01 BST

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A Paraconsistent Higher Order Logic

by J?rgen Villadsen

Classical logic predicts that everything (thus nothing useful at all) follows from inconsistency. A paraconsistent logic is a logic where an inconsistency does not lead to such an explosion, and since in practice consistency is difficult to achieve there are many potential applications of paraconsistent logics in knowledge-based systems, logical semantics of natural language, etc. Higher order logics have the advantages of being expressive and with several automated theorem provers available. Also the type system can be helpful. We present a concise description of a paraconsistent higher order logic with countable infinite indeterminacy, where each basic formula can get its own indeterminate truth value (or as we prefer: truth code). The meaning of the logical operators is new and rather different from traditional many-valued logics as well as from logics based on bilattices. The adequacy of the logic is examined by a case study in the domain of medicine. Thus we try to build a bridge between the HOL and MVL communities. A sequent calculus is proposed based on recent work by Muskens.
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Posted by Tony Marmo at 01:01 BST

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