Logical Form

In the unpublished work Theory of Knowledge† a complex is assumed to be “anything analyzable, any- thing which has constituents” (p. 79), and analysis is presented as the “discovery of the constituents and the manner of combination of a given complex” (p. 119). The notion of complex is linked in various ways with the notions of relating relation, logical form and proposition, taken as a linguistic expression provided with meaning. This paper mainly focuses on these notions, on their links and, more widely, on the role of logical form, by offering a new way of understanding what Russell was doing in TK as concerns the logical-ontological matter of this manuscript. In particular, a new account of Russell's theory of judgment will be given, by taking a stand with respect to the main accounts already given, and it will be argued for the presence in TK of a notion of type different from the one applied to propositional functions in ML and PM.

The tremendous success of the World Wide Web is countervailed by efforts needed to search and find relevant information. For tabular structures embedded in HTML documents typical keyword or link-analysis based search fails. The Semantic Web relies on annotating resources such as documents by means of ontologies and aims to overcome the bottleneck of finding relevant information. Turning the current Web into a Semantic Web requires automatic approaches for annotation since manual approaches will not scale in general. Most efforts have been devoted to automatic generation of ontologies from text, but with quite limited success. However, tabular structures require additional efforts, mainly because understanding of table contents requires a table structures comprehension task and a semantic interpretation task, which exceeds in complexity the linguistic task. The focus of this paper is on automatic transformation and generation of semantic (F-Logic) frames from table-like structures. The presented work consists of a methodology, an accompanying implementation (called TARTAR) and a thorough evaluation. It is based on a grounded cognitive table model which is stepwise instantiated by the methodology. A typical application scenario is the automatic population of ontologies to enable query answering over arbitrary tables (e.g. HTML tables).

The paper presents an outline of a unified answer to five questions concerning logic: (1) Is logic in the mind or in the world? (2) Does logic need a foundation? What is the main obstacle to a foundation for logic? Can it be overcome? (3) How does logic work? What does logical form represent? Are logical constants referential? (4) Is there a criterion of logicality? (5) What is the relation between logic and mathematics?

In this paper, Ockham's theory of an ideal language of thought is used to illuminate problems of interpretation of his theory of truth. The twentieth century idea of logical form is used for finding out what kinds of atomic sentences there are in Ockham's mental language. It turns out that not only the theory of modes of supposition, but also the theory of supposition in general is insufficient as a full theory of truth. Rather, the theory of supposition is a theory of reference, which can help in the determination of truth values within the scope of simple predications. Outside this area, there are interesting types of sentences, whose truth does not depend on whether the terms supposit for the same things or not for the same things.

This volume continues the discussion initiated in Part 1 of "Logical Forms" and deals with issues of language, logic, proof, and knowledge. I list the chapter titles:
13. Language, meaning, and reference.
14. Syntax and semantics.
15 Grammar and logical form.
16. Propositional logic.
17. Predicate logic.
18. Grammar and logical truth.
19. Proof and logical deduction.
20. Proof and proving.
21. Proof and truth.
22. The tyranny of belief.
23. Ockham's razor.
24. Knowledge and justification.
25. Logic and knowledge.
Epilogue. Plato, Zeno, Parmenides, and Frege.

A translation to Portuguese of chapter 25--Lógica e conhecimento--was published in 2007 and I added the pdf in TRANSLATIONS.

This volume breaks new grounds b< bringing together a great variety of innovative contributions on triangulation, epistemology, and mind. The notion of "triangulation", developed by Donald Davidson (1917-2003) during the last two decades of his life, has changed our understanding of the relationship between subjective, intersubjective, and objective , and shed new light on concepts such as externalism, internalism, communication, interpretation, and language.

At the same time, however, it has been strongly criticized for several aspöects. The papers collected in this volume—wirtten by established contributors—aim to provide new insights into the contemporary debate on  triangulation. The upshot is not only a deeper understanding of Davidson's ideas but also a new apprecciation of some central problems of epistemology and the philosophy of mind with regard to adjoining disciplines auch as, for instance, cognitive sciences and the philosophy of language.

In the file:

Contents
Introduction
--
The Externalism of Triangulation
Gerhard Preyer

I analyze Russell's account of the nature of relations (internal vs. external) and its logical, epistemological and metaphysical implications. In doing this, I also consider the problems of the unity of propositions, of their logical analysis and of the threat of Bradley's regress. I argue that Russell struggled with these problems for years, never achieving a completely coherent position. Indeed he abandoned his first and radical position , which seemed to be threaten by Bradley's regress; a more soft account, akin to Frege's and Wittgenstein's account of the unity of proposition, though immune from that regress, was compromised with forms of molecularism, by Russell considered depending from internal relations and Idealism.

Il Tractatus logico-philosophicus di Wittgenstein attribuisce una forma ad entità a prima vista disparate: gli oggetti semplici; la realtà nel suo complesso; le proposizioni. In questo libro, Giorgio Lando pone la teoria della forma al centro delle tesi metafisiche e semantiche del giovane Wittgenstein. A partire da questa intuizione, molti temi spesso discussi isolatamente dagli interpreti possono essere interpretati in modo unitario e coerente: la “soluzione” del problema di Bradley sulle relazioni; il cosidetto “pensiero fondamentale”, secondo cui la logica dei fatti non può avere rappresentanti; le ragioni della composizionalità semantica; i vincoli sulla natura degli oggetti semplici. Questa ricostruzione mostra che la crescente tendenza a considerare Wittgenstein come una figura irriducibilmente peculiare o come un ironista dedito solo a denunciare le insensatezze della metafisica è fuori strada: il Tractatus può essere utilmente analizzato e criticato con gli strumenti teorici della metafisica analitica contemporanea. Il volume contiene una prefazione di Pasquale Frascolla.

In this paper, I claim that the main reason why we should study (and teach) logic, at any level of education,  is that what we call "logic" sometimes is simply wrong. More specifically: the forms that guide our reasoning sometimes make us believe falsity. However, not any teaching of "logic" can help us to avoid logical mistakes. I argue that the kind of (study of) logic that should be potentiated and promoted, not only for mathematicians or philosophers, but for everyone, is philosophical logic.

This paper shows why the non-trivial zeros of the Riemann zeta function ζ must always be on the critical line Re(s) = 1/2 and not anywhere else on the critical strip bounded by Re(s) = 0 and Re(s) = 1, thus affirming the validity of the Riemann hypothesis. MSC: 11-XX (Number Theory)

Corcoran, J. 1989. Argumentations and Logic. Argumentation 3: 17-43

Argumentations are at the heart of the deductive and the hypothetico-deductive methods, which are involved in attempts to reduce currently open problems to problems already solved.  These two methods span the entire spectrum of problem-oriented reasoning from the simplest and most practical to the most complex and most theoretical, thereby uniting all objective thought whether ancient or contemporary, whether humanistic or scientific, whether normative or descriptive, whether concrete or abstract.  Analysis, synthesis, evaluation, and function of argumentations are described.  Perennial philosophic problems, epistemic and ontic, related to argumentations are put in perspective.  So much of what has been regarded as logic is seen to be involved in the study of argumentations that logic may be usefully defined as the systematic study of argumentations, which is virtually identical to the quest of objective understanding of objectivity.

KEY WORDS: hypothesis, theorem, argumentation, proof, deduction, premise-conclusion argument, valid, inference, implication, epistemic, ontic, cogent, fallacious, paradox, formal, validation.

“Argumentations and Logic” has been used in courses at University of Barcelona, Bryn Mawr College, University of Buffalo, Buffalo State College, State University of Campinas, Canisius College, Federal University of Goiás, Fredonia University, Grand Valley State University, University of Lausanne, Niagara University, University of Santiago de Compostela, SUNY Potsdam, and elsewhere.
It has been translated into Spanish, Portuguese, and Persian. Insha’Allah, in the fullness of time there will be translations into Chinese and Czech.

This paper shows why the non-trivial zeros of the Riemann zeta function ζ will always be on the critical line Re(s) = 1/2 and not anywhere else on the critical strip bounded by Re(s) = 0 and Re(s) = 1, thus affirming the validity of the Riemann hypothesis. [The paper is published in a journal of number theory.]

This paper investigates wh-in-situ questions in Najdi Arabic. It documents the distribution of in-situ wh-phrases in Najdi Arabic and compares it to Lebanese Arabic (Aoun, Benmamoun, and Choueiri 2010). It also discusses the two major analyses for wh-in-situ languages: LF movement and the unselective binding analysis. Island insensitivity of wh-in-situ in Najdi supports the unselective binding analysis. The paper concludes by showing that selectional restriction data that originally used in favor of the LF movement approach can also be accounted for with unselective binding.

The main purpose of this paper is to discuss the origin and the bounds of the schematic hylomorphism in ancient and medieval logic. The sub-purposes are fourfold. Firstly, various explications of the logical hylomorphism will be illustrated. Secondly, I propose to reevaluate certain interpretations of Aristotle’s syllogistic. I attempt to answer the question why Aristotle was not the founder of logical hylomorphism. Thirdly, I aim to qualify the schematic hylomorphism of Alexander of Aphrodisias. Finally, I focus on the medieval discussions on syncategoremata and formal consequences.DOI: 10.21146/2074-1472-2016-22-2-59-72

Distributed Shared Memory (DSM) systems provide a logically shared memory over physically distributed memory to enable parallel computation on Networks of Workstations (NOWs). In this paper, we propose an infrastructure for DSM systems to utilize idle cycles in the network by thread migration.

This paper compares performance of a linguistically motivated probabilistic context free grammar-based (L-PCFG) language model against a base line class ngram-based language model on data from a medium vocabulary application, the Clarissa International Space Station procedure navigator domain. The Regulus open source package makes this possible by providing a trainable method for constructing domain specific grammars with logical-form semantics. We construct L-PCFG-based and n-gram language models from the same corpus for comparison, and find that the L-PCFGbased language model provides better performance in this domain. The best n-gram version has a semantic error rate of 9.6%, while the best GLM version has an error rate of 6.0%. Part of this advantage is accounted for by the superior WER and Sentence Error Rate (SER) of the GLM (WER 7.42% versus 6.27%, and SER 12.41% versus 9.79%). The rest is most likely accounted for by the fact that the L-PCFG architecture is able to use logical-form-based features, which permit tighter integration of recognition and semantic interpretation.

The paper argues that by modelling the incremental and left-right process of interpretation as a process of growth of logical form (representing logical forms as trees), an integrated typology of left-dislocation and right-dislocation phenomena becomes available, bringing out not merely the similarities between these types of phenomena, but also their asymmetry. The data covered include hanging topic left dislocation, clitic left dislocation, left dislocation, pronoun doubling, expletives, extraposition, and right node raising, with each set of data analysed in terms of general principles of tree growth. In the light of the success in providing a characterisation of the asymmetry between left and right periphery phenomena, a result not achieved in more wellknown formalisms, the paper concludes that grammar formalisms should model the dynamics of language processing in time.Article

This article proposes a novel technique to generate natural language descriptions for a wide class of relational database queries. The approach to describing queries is phrasal and is restricted to a class of queries that return only whole schema tuples as answers. Query containment and equivalence are decidable for this class and this property is exploited in the maintenance and use of a phrasal lexicon. The query description mechanism is implemented within the STEP (Schema Tuple Query Processor) system (http://www.cs.umu.se/∼mjm/step).

Simulating human language understanding on the computer is a great challenge. A way to approach it is to represent natural language meanings in logic, and to use logical provers to determine what does and does not follow from a text. What logic is best to use and how natural language meanings are best represented in it are far from trivial questions. This thesis focuses on semantic representation in deep parsing. It describes the Delilah parser and generator for Dutch, which computes semantic representations for sentences, discussing several issues and proposing some further improvements to the system. A style of logical form is developed that is optimized for inference in mainly two ways. One is the implementation of event semantics for verbs and nominalizations and with underlying states for intersective adjectives and their corresponding abstract nouns. This makes many entailments follow straightforwardly. The second is the introduction of Flat Logical Form, as an alternative to ...

In the article the structure of the negative clauses in Czech has been iscussed with respect to different types of clauses. We started from the typological observations conceming the possible means of expressing negation in the world languages as weil as their different structural.
Mostly,the negation is expressed by a bound morpheme (e.g. prefix or suffix), a negative auxiliary, a clitic like a head or an adverb. The most prominent negated sentences in Czech tumed out to be those in which a lexical independent functional projection with Neg as a head is assurned. Furthermore, some universal and specific properties of sentential negation as pposed to those of constituent negation were discussed. In the subsequent chapters, a closer look was taken at the negation related phenomena, namely Genitive of negation and negative pronouns (negative concord).

One crucial result of this article was that sentential negation must be located in the vicinity of the Accusative case checker, i.e. in some position above vP. The im of the subsequent section was to establish the precise position of negation in the clause. Doing so we established crucial differences between modal
and auxiliary verbs assuming that modal constructions are best analyzed as biclausal, consequently the negation occuring in the matrix or the complement clause has the properties of sentential negation. Finally, the last section focused on the
question of whether there is a NegP in Czech. The result of our investigation is the proposal that sentence negation is a proclitic heading of its own functional projection NegP.

I will suggest, in this article, a possible explanation of the fact that legal language appears incoherent to the general public. I will present one legal text (an indictment), explaining why it appears incoherent to legal laypersons. I will argue that the traits making ...

There is almost a consensus among conditional experts that indicative conditionals are not material. Their thought hinges on the idea that if indicative conditionals were material, A → B could be vacuously true when A is false, even if B would be false in a context where A is true. But since this consequence is implausible, the material account is usually regarded as false. It is argued that this point of view is motivated by the grammatical form of conditional sentences and the symbols used to represent their logical form, which misleadingly suggest a one-way inferential direction from A to B. That conditional sentences mislead us into a directionality bias is a phenomenon that is well-documented in the literature about conditional reasoning. It is argued that this directional appearance is deceptive and does not reflect the underlying truth conditions of conditional sentences. This directional bias is responsible for both the unpopularity of the material account of conditionals and some of the main alternative principles and themes in conditional theory, including the Ramsey’s test, the Equation, Adams’ thesis, conditional-assertion and possible world theories. The directional mindset forgets a hard- earned lesson that made classical logic possible in the first place, namely, that grammatical form of sentences can mislead us about its truth conditions. There is a case to be made for a material account of indicative conditionals when we break the domination of words over the human mind.

Abstract Guillermo Rosado-Haddock:
In this paper on Oswaldo Chateaubriand's book Logical Forms I, I am mostly concerned with the critical task of indicating some shortcomings and stressing my disagreements with the distinguished scholar. The most important shortcoming of the book is Chateaubriand's unfamiliarity with Husserl's views on logic and semantics, some of which anticipate views propounded by the former--e.g., the distinction between logical law and logical necessity--, whereas others are more subtle than Chateaubriand's views--e.g. Husserl's views on the referent of statements. One of the most important contributions of Chateaubriand's book is his analysis and rejection of all forms of the so-called "slingshot argument". On the other hand, I disagree with Chateaubriand's rendering of some of Frege's views, though some of these are very common among Frege scholars. Finally, I assess Chateaubriand's criticisms of Kripke's views as well as those of Tarski. I tend to agree with his criticism of Kripke, but disagree with his assessment of Tarskian semantics.

Abstract response:
In §§1-2 I consider some issues that Guillermo raises in connection with Husserl, especially the distinction between the notion of state of affairs and the more general notion of situation of affairs conceived as a common substratum for different states of affairs. After a few remarks about Church’s slingshot argument in §3, I discuss several objections that Guillermo raises to my interpretation of Frege (§4), to Kripke’s notion of rigid designator (§5) and to my objections to Tarski’s semantic conception of truth (§6).

Many researchers believe that certain aspects of natural language processing, such as word sense disambiguation and plan recognition in stories, constitute abductive inferences. We have been working with a specific model of abduction, called parsimonious covering, ap­ plied in diagnostic problem solving, word sense disambiguation and logical form generation in some restricted settings. Diagnostic parsimo­ nious covering has been extended into a dual- route model to account for syntactic and se­ mantic aspects of natural language. The two routes of covering are integrated by defining &quot;open class&quot; linguistic concepts, aid­ ing each other. The diagnostic model has dealt with sets, while the extended version, where syntactic considerations dictate word or­ der, deals with sequences of linguistic concepts. Here we briefly describe the original model and the extended version, and briefly characterize the notions of covering and different criteria of parsimony. Finally we examine...

We present a method for extracting sentences from an individual document to serve as a document summary or a pre-cursor to creating a generic document abstract. We apply syntactic analysis of the text that produces a logical form analysis for each sentence. We use subject–object–predicate (SOP) triples from individual sentences to create a semantic graph of the original document and the corresponding human extracted summary. Using the Support Vector Machines learning algorithm, we train a classifier to identify SOP ...

This is a paper versions of which I have presented at Denison University, Edinburgh, and UC Irvine. It has been improved by comments from all three audiences. It may be ready to send somewhere.
The basic idea is that essentialism is correct, except that there is not a single articulation of reality into objects. Articulation into objects is something we do, not something that is intrinsic to reality.