We study a new formal logic LD introduced by Prof. Grzegorczyk. The logic is based on so-called descriptive equivalence, corresponding to the idea of shared meaning rather than shared truth value. We construct a semantics for LD based on a new type of algebras and prove its soundness and completeness. We further show several examples of classical laws that hold for LD as well as laws that fail. Finally, we list a number of open problems. -/- .

This paper uses classical logic for a simultaneous description of the syntax and semantics of a fragment of English and it is argued that such an approach to natural language allows procedural aspects of linguistic theory to get a purely declarative formulation. In particular, it will be shown how certain construction rules in Discourse Representation Theory, such as the rule that indefinites create new discourse referents and definites pick up an existing referent, can be formulated declaratively if logic is (...) used as a metalanguage for English. In this case the declarative aspects of a rule are highlighted when we focus on the model theory of the description language while a procedural perspective is obtained when its proof theory is concentrated on. Themes of interest are Discourse Representation Theory, resolution of anaphora, resolution of presuppositions, and underspecification. (shrink)

An attractive way to model the relation between an underspecified syntactic representation and its completions is to let the underspecified representation correspond to a logical description and the completions to the models of that description. This approach, which underlies the Description Theory of Marcus et al. 1983 has been integrated in Vijay-Shanker 1992 with a pure unification approach to Lexicalized Tree-Adjoining Grammars (Joshi et al. 1975, Schabes 1990). We generalize Description Theory by integrating semantic (...) information, that is, we propose to tackle both syntactic and semantic underspecification using descriptions. (shrink)

In Groenendijk & Stokhof [1989] a system of dynamic predicate logic (DPL) was developed, as a compositional alternative for classical discourse representation theory (DRT ). DPL shares with DRT the restriction of being a first-order system. In the present paper, we are mainly concerned with overcoming this limitation. We shall define a dynamic semantics for a typed language with λ-abstraction which is compatible with the semantics DPL specifies for the language of first-order predicate logic. We shall propose to use this (...) new logical system as the semantic component of a Montague-style grammar (referred to as dynamic Montague grammar, DMG), which will enable us to extend the compositionality of DPL to the subsentential level. Furthermore, we shall extend this analysis also in this sense that we shall add new, dynamic interpretations for logical constants which in DPL were treated in a static fashion. This will substantially increase the descriptive coverage of DMG. (shrink)

This essay critically assesses Roman Ingarden’s 1915 review of the second edition of Edmund Husserl’s Logical Investigations. I elucidate and critique Ingarden’s analysis of the differences between the 1901 first edition and the 1913 second edition. I specifically examine three tenets of Ingarden’s interpretation. First, I demonstrate that Ingarden correctly denounces Husserl’s claim that he only engages in an eidetic study of consciousness in 1913, as Husserl was already performing eidetic analyses in 1901. Second, I show that Ingarden is (...) misguided, when he asserts that Husserl had fully transformed his philosophy into a transcendental idealism in the second edition. While Husserl does appear to adopt a transcendental phenomenology by asserting–in his programmatic claims–that the intentional content and object are now included in his domain of research, he does not alter his actual descriptions of the intentional relationship in any pertinent manner. Third, I show Ingarden correctly predicts many of the insights Husserl would arrive at about logic in his late philosophy. This analysis augments current readings of the evolution of Ingarden’s philosophy, by more closely examining the development of his largely neglected early thought. I execute this critical assessment by drawing both from Husserl’s later writings and from recent literature on the Investigations. By doing so, I hope to additionally demonstrate how research on the Investigations has matured in the one hundred years since the release of that text, while also presenting my own views concerning these difficult interpretative issues. (shrink)

This paper demonstrates that Edmund Husserl’s frequently overlooked 1890 manuscript, “On the Logic of Signs,” when closely investigated, reveals itself to be the hermeneutical touchstone for his seminal 1891 Philosophy of Arithmetic. As the former comprises Husserl’s earliest attempt to account for all of the different kinds of signitive experience, his conclusions there can be directly applied to the latter, which is focused on one particular type of sign; namely, number signs. Husserl’s 1890 descriptions of motivating and replacing signs will (...) be respectively employed to clarify his 1891 understanding of the authentic and inauthentic presentations of numbers via number signs. Moreover, his schematic classification of replacement-signs in Semiotic will illuminate the reasons why he believed the number system to be necessary for the operation of replacing number signs. (shrink)

When one looks into the role of artificial languages in philosophy of language it seems appropriate to start with making a distinction between philosophy of language proper and formal semantics of natural language. Although the distinction between the two disciplines may not always be easy to make since there arguably exist substantial historical and systematic relationships between the two, it nevertheless pays to keep the two apart, at least initially, since the motivation commonly given for the use of artificial languages (...) in philosophy of language is often rather different from the one that drives the use of such languages in semantics. Of course, this difference in motivation should not blind us for the commonalities that exists between the two disciplines. Philosophy of language and formal semantics have a common history, and arguably also share some of their substance. Philosophy of language is by and large an outgrowth of work in the analytical tradition in philosophy in the first half of the twentieth century. Both ordinary language philosophy, with its emphasis on the description of actual language use, as well as the more logic-oriented and formally inclined school of logical positivism contributed to the definition of philosophy of language as a separate philosophical discipline, with its own set of problems and methods to solve them. Another major contributor to the establishment of philosophy of language as a distinct discipline has been modern linguistics, in particular generative grammar in the tradition of Chomsky that became the dominant paradigm in linguisticsin the fifties and sixties of the previous century. And as it happens, both the generative tradition of Chomsky and analytic philosophy in its formal and less formal guises have been important factors in the development of formal semantics as well. Thus, it should come as no surprise that the two have something in common. That the communalities go beyond a common ancestry, but are reflected in substance and methods as well, will be argued later on. However, be that as it may, it is still a good idea to keep philosophy of language and formal semantics separate, at least initially, since the role that is assigned to artificial languages and the ways in which these languages are employed in both does differ in a number of respects that are worth keeping in mind.. (shrink)

This implies that something cannot be both a rule of grammar and at the same time a description of reality. This approach leaves the religious language game forever defining its own rules. The question is then prompted that if religious language does not get beyond itself to explore reality, how did it get started at all. -/- The fundamental reason that I myself stick to the idea that there are right and wrong moral judgments and better and worse moral (...) outlooks, and also right and wrong evaluative judgments and better and worse normative outlooks in areas other than morality, is not a metaphysical one. The reason is simply that that is the way that we—and I include myself in this \"we\"—talk and think, and also the way that we are going to go on talking and thinking. -/- Hume confessed that he left his scepticism about the material world behind as soon as he left his study; and I observe that no matter how sceptical or how relativistic philosophers may be in their conversation, they leave their scepticism or their relativism behind the minute they engage in serious discussion about almost any subject other than philosophy. (shrink)

We propose a nonmonotonic Description Logic of typicality able to account for the phenomenon of the combination of prototypical concepts. The proposed logic relies on the logic of typicality ALC + TR, whose semantics is based on the notion of rational closure, as well as on the distributed semantics of probabilistic Description Logics, and is equipped with a cognitive heuristic used by humans for concept composition. We first extend the logic of typicality ALC + TR by typicality inclusions (...) of the form p :: T(C) v D, whose intuitive meaning is that “we believe with degree p about the fact that typical Cs are Ds”. As in the distributed semantics, we define different scenarios containing only some typicality inclusions, each one having a suitable probability. We then exploit such scenarios in order to ascribe typical properties to a concept C obtained as the combination of two prototypical concepts. We also show that reasoning in the proposed Description Logic is EXPTIME-complete as for the underlying standard Description Logic ALC. (shrink)

We propose a nonmonotonic Description Logic of typicality able to account for the phenomenon of combining prototypical concepts, an open problem in the fields of AI and cognitive modelling. Our logic extends the logic of typicality ALC + TR, based on the notion of rational closure, by inclusions p :: T(C) v D (“we have probability p that typical Cs are Ds”), coming from the distributed semantics of probabilistic Description Logics. Additionally, it embeds a set of cognitive heuristics (...) for concept combination. We show that the complexity of reasoning in our logic is EXPTIME-complete as in ALC. (shrink)

My aims are exegetical rather than critical: I offer a systematic account of Hursthouse's ethical naturalism with an emphasis on the normative authority of the four ends, and try to correct some misconceptions found in the literature. Specifically, I argue that the four ends function akin to Wittgensteinian hinge-propositions for our practice of ethical reasoning and as such form part of a description of the logical grammar of said practice.

This paper presents rules of inference for a binary quantifier I for the formalisation of sentences containing definite descriptions within intuitionist positive free logic. I binds one variable and forms a formula from two formulas. Ix[F, G] means ‘The F is G’. The system is shown to have desirable proof-theoretic properties: it is proved that deductions in it can be brought into normal form. The discussion is rounded up by comparisons between the approach to the formalisation of definite descriptions recommended (...) here and the more usual approach that uses a term-forming operator ι, where ιxF means ‘the F’. (shrink)

I summarize several of the main claims, arguments, and innovations in Stojnić's 2021 book. I then take issue with her foundational view, on which both the context of a conversation and the contents of context-sensitive expressions are wholly fixed by the history of a conversation together with grammatical rules.

Sentences containing definite descriptions, expressions of the form ‘The F’, can be formalised using a binary quantifier ι that forms a formula out of two predicates, where ιx[F, G] is read as ‘The F is G’. This is an innovation over the usual formalisation of definite descriptions with a term forming operator. The present paper compares the two approaches. After a brief overview of the system INFι of intuitionist negative free logic extended by such a quantifier, which was presented in (...) (Kürbis 2019), INFι is first compared to a system of Tennant’s and an axiomatic treatment of a term forming ι operator within intuitionist negative free logic. Both systems are shown to be equivalent to the subsystem of INFι in which the G of ιx[F, G] is restricted to identity. INFι is then compared to an intuitionist version of a system of Lambert’s which in addition to the term forming operator has an operator for predicate abstraction for indicating scope distinctions. The two systems will be shown to be equivalent through a translation between their respective languages. Advantages of the present approach over the alternatives are indicated in the discussion. (shrink)

In computational complexity theory, decision problems are divided into complexity classes based on the amount of computational resources it takes for algorithms to solve them. In theoretical computer science, it is commonly accepted that only functions for solving problems in the complexity class P, solvable by a deterministic Turing machine in polynomial time, are considered to be tractable. In cognitive science and philosophy, this tractability result has been used to argue that only functions in P can feasibly work as computational (...) models of human cognitive capacities. One interesting area of computational complexity theory is descriptive complexity, which connects the expressive strength of systems of logic with the computational complexity classes. In descriptive complexity theory, it is established that only first-order (classical) systems are connected to P, or one of its subclasses. Consequently, second-order systems of logic are considered to be computationally intractable, and may therefore seem to be unfit to model human cognitive capacities. This would be problematic when we think of the role of logic as the foundations of mathematics. In order to express many important mathematical concepts and systematically prove theorems involving them, we need to have a system of logic stronger than classical first-order logic. But if such a system is considered to be intractable, it means that the logical foundation of mathematics can be prohibitively complex for human cognition. In this paper I will argue, however, that this problem is the result of an unjustified direct use of computational complexity classes in cognitive modelling. Placing my account in the recent literature on the topic, I argue that the problem can be solved by considering computational complexity for humanly relevant problem solving algorithms and input sizes. (shrink)

We generalize intuitionistic tense logics to the multi-modal case by placing grammar logics on an intuitionistic footing. We provide axiomatizations for a class of base intuitionistic grammar logics as well as provide axiomatizations for extensions with combinations of seriality axioms and what we call "intuitionistic path axioms". We show that each axiomatization is sound and complete with completeness being shown via a typical canonical model construction.

The sentences ‘p but I don’t believe p’ (omissive form) and ‘p but I believe that not-p’ (comissive form) are typical examples of Moore’s paradox. When an agent (sincerely) asserts such sentences under normal circumstances, we consider his statements absurd. The Simple Solution (Moore, Heal, Wolgast, Kriegel, et al.) finds the source of absurdity for such statements in a certain formal contradiction (some kind of like ‘p & not-p’), the presence of which is lexically disguised. This solution is facing criticism (...) since it is obvious that the denial of the contradiction allegedly hidden in Moore’s paradox will not become an expression of tautology for us. Hintikka offers another solution to Moore’s paradox. In his view, the source of absurdity is the practical inconceivability of the situation, in which the agent would be able to hold mutually incompatible (inconsistent) beliefs. The sentences ‘p but I don’t believe that p’ and ‘p but I believe that not-p’ sound absurd because they express high-ordered beliefs that no rational agent can hold. A belief expressed in the sentence ‘he believes that p’, in order to be available to the agent, must be compatible with the truth of everything the agent believes. The problem with Hintikka’s solution is that it relies on an epistemic principle that does not correspond to our general intuitions about the notion of belief. According to this principle, there must be a close connection between the sentence ‘p but I don’t believe that p’ and the sentence ‘I believe that is the case is that p but I don’t believe that p’. However, it is not difficult to imagine the context for situations when the agent asserts the sentence ‘p but I don’t believe that p’ when s/he believes that p, but in parallel does not hold any high-ordered belief about his/her belief in p. For example, the agent does not recognize oneself in a photograph after a hard plastic surgery, and when one asks him ‘who is this?’ it would not be absurd for him/her to accept the following description of his/her beliefs ‘I believe that {I am me} but I don’t believe that I believe that {I am me}’. Wittgenstein provides an alternative solution based on a descriptive analysis of the grammar of verbs we use to express, attribute, and understand each other’s psychological states. In his view, the everyday practice of using the verb ‘believe’ demonstrates a characteristic asymmetry in the semantic and logical properties of the usage of this verb in the first person. The expression ‘I believe falsely’ has no real meaning since no one can meaningfully say the sentence ‘Now I believe falsely that p’ on their own behalf. Therefore, the genuine source of absurdity is associated with situations of self-attribution of false belief by the agent. Despite its originality, Wittgenstein’s solution faces objections. For example, in a certain context, it would not be absurd to assert the sentence ‘There are no beliefs, but I don’t believe in it’, unlike the sentence ‘There are no beliefs and I believe that it is so’. The solution proposed by Wittgenstein does not allow us to correct the situation since one could assert quite reasonably and without any absurdity a sentence like ‘In fact, there are no beliefs and now I falsely believe that it is so’. Based on Evans’ principle of epistemic transparency, some researchers (Atlas, Chan, Kwon, et al.) offer another strategy for solving Moore’s paradox, in which peculiar attention is paid to the dependence of understanding and evaluating the meaning of the sentences ‘p but I do not believe that p’ and ‘p but I believe that not-p’ from the immediate context of their usage. The source of absurdity should be looked for in the established practice of the self-referential use of the pronoun ‘I’. In the researchers’ view, Moore’s paradox arises only in the context of situations where the agent asserting such sentences is conscious speaking about oneself. Therefore, there is an obvious structural analogy between the sentences of the Liar family (‘This very sentence is false’, ‘Now I am lying’, etc.) and Moore’s paradox (‘p but I don’t believe that p’, ‘p but I believe that not-p’) – self-reference is constitutive for both families of paradoxical statements. (shrink)

Description Logics (DLs) are a family of well-known terminological knowledge representation formalisms in modern semantics-based systems. This research focuses on analysing how our developed Occurrence Logic (OccL) can conceptually and logically support the development of a description logic. OccL is integrated into the alternative theory of natural language syntax in `Deviational Syntactic Structures' under the label `EFA(X)3' (or the third version of Epi-Formal Analysis in Syntax, EFA(X), which is a radical linguistic theory). From the logical point of (...) view, OccL is a formal logic that mainly deals with the occurrences of symbols as well as with their priorities within linguistic descriptions, i.e. natural language syntax, semantics and phonology. In this article---based on our OccL-based definitions of the concepts of `strong implication' and `occurrence value' as well as of the logical concept `identical occurrence constructor (IDOC)' that is the most fundamental logical concept in our formalism---we will model Occurrence Description Logic ($\mathcal{ODL}$). Accordingly, we will formally-logically analyse `occurrence(s) of symbol(s)' within descriptions of the world in $\mathcal{ODL}$. In addition, we will analyse and assess the logical concepts of `occurrence' and `occurrence priority' in $\mathcal{ODL}$. This research can make a strong logical background for our future research in the development of a Modal Occurrence Description Logic. (shrink)

This paper accomplishes two goals. First, I elucidate Edmund Husserl’s theory of inauthentic judgments from his 1890 “On the Logic of Signs (Semiotic).” It will be shown how inauthentic judgments are distinct from other signitive experiences, in such a manner that when Husserl seeks to account for them, he is forced to revise the general structure of his philosophy of meaning and in doing so, is also able to realize novel insights concerning the nature of signification. Second, these conclusions are (...) revealed to be the foundation of Husserl’s pure logical grammar, found in the 1901 “Fourth Logical Investigation.” In his analysis of inauthentic judgments, Husserl already recognized, albeit in a problematic way and for entirely different reasons, many of the central tenets of the 1901 work concerning categoremata and syncategoremata, matter and form, and the isomorphism between them. (shrink)

Logical analysis of the applicability of nominals (which are introduced by hybrid logic) in the formal descriptions of the world (within modern knowledge representation and semantics-based systems) is very important because nominals, as second sorts of propositional symbols, can support logical identification of the described world at specific [temporal and/or spacial] states. This paper will focus on answering the philosophical-logical question of ‘how a fundamental world description in description logic (DL) and a nominal can be (...) related to each other?’. Based on my assumption that nominals can support more adequate identification of the world in DL, this paper will deal with the concept of ‘world identification’. Accordingly, based on a logical-terminological analysis of nominals, the paper will analyse hybridised fundamental world descriptions. The research will finally reach the idea that we can have a hybrid description logic based on the analysed concepts. (shrink)

This paper proves normalisation theorems for intuitionist and classical negative free logic, without and with the $\invertediota$ operator for definite descriptions. Rules specific to free logic give rise to new kinds of maximal formulas additional to those familiar from standard intuitionist and classical logic. When $\invertediota$ is added it must be ensured that reduction procedures involving replacements of parameters by terms do not introduce new maximal formulas of higher degree than the ones removed. The problem is solved by a rule (...) that permits restricting these terms in the rules for $\forall$, $\exists$ and $\invertediota$ to parameters or constants. A restricted subformula property for deductions in systems without $\invertediota$ is considered. It is improved upon by an alternative formalisation of free logic building on an idea of Ja\'skowski's. In the classical system the rules for $\invertediota$ require treatment known from normalisation for classical logic with $\lor$ or $\exists$. The philosophical significance of the results is also indicated. (shrink)

Husserl and Frege on the analysis of the concept of number and primitive logical concepts.

The positions of Frege, Russell and Wittgenstein on the priority of complexes over (propositional) functions are sketched, challenging those who take the "judgment centered" aspects of the Tractatus to be inherited from Frege not Russell. Frege's views on the priority of judgments are problematic, and unlike Wittgenstein's. Russell's views on these matters, and their development, are discussed in detail, and shown to be more sophisticated than usually supposed. Certain misreadings of Russell, including those regarding the relationship between propositional functions and (...) universals, are exposed. Wittgenstein's and Russell's views on logical grammar are shown to be very similar. Russell's type theory does not countenance types of genuine entities nor metaphysical truths that cannot be put into words, contrary to conventional wisdom. I relate this to the debate over "inexpressible truths" in the Tractatus. I lastly comment on the changes to Russell's views brought about by Wittgenstein's influence. (shrink)

We intoduce a novel extension of Description Logics (DLs) of typicality by means of probabilities able to represent and reason about typical properties and defeasible inheritance in DLs.

This paper presents a way of formalising definite descriptions with a binary quantifier ι, where ιx[F, G] is read as ‘The F is G’. Introduction and elimination rules for ι in a system of intuitionist negative free logic are formulated. Procedures for removing maximal formulas of the form ιx[F, G] are given, and it is shown that deductions in the system can be brought into normal form.

The van Wijngaarden grammars are two-level grammars that present many interesting properties. In the present article I elaborate on six of these properties, to wit, (i) their being constituted by two grammars, (ii) their ability to generate (possibly infinitely many) strict languages and their own metalanguage, (iii) their context-sensitivity, (iv) their high descriptive power, (v) their productivity, or the ability to generate an infinite number of production rules, and (vi) their equivalence with the unrestricted, or Type-0, Chomsky (...) grammars. (shrink)

This paper accomplishes two goals. First, I elucidate Edmund Husserl’s theory of inauthentic judgments from his 1890 “On the Logic of Signs.” It will be shown how inauthentic judgments are distinct from other signitive experiences, in such a manner that when Husserl seeks to account for them, he is forced to revise the general structure of his philosophy of meaning and in doing so, is also able to realize novel insights concerning the nature of signification. Second, these conclusions are revealed (...) to be the foundation of Husserl’s pure logical grammar, found in the 1901 “Fourth Logical Investigation.” In his analysis of inauthentic judgments, Husserl already recognized, albeit in a problematic way and for entirely different reasons, many of the central tenets of the 1901 work concerning categoremata and syncategoremata, matter and form, and the isomorphism between them. (shrink)

Ontology is currently perceived as the solution of first resort for all problems related to biomedical terminology, and the use of description logics is seen as a minimal requirement on adequate ontology-based systems. Contrary to common conceptions, however, description logics alone are not able to prevent incorrect representations; this is because they do not come with a theory indicating what is computed by using them, just as classical arithmetic does not tell us anything about the entities that are (...) added or subtracted. In this paper we shall show that ontology is indeed an essential part of any solution to the problems of medical terminology – but only if it is understood in the right sort of way. Ontological engineering, we shall argue, should in every case go hand in hand with a sound ontological theory. (shrink)

We present some ideas on logical process descriptions, using relations from the DIO (Drug Interaction Ontology) as examples and explaining how these relations can be naturally decomposed in terms of more basic structured logical process descriptions using terms from linear logic. In our view, the process descriptions are able to clarify the usual relational descriptions of DIO. In particular, we discuss the use of logical process descriptions in proving linear logical theorems. Among the types of reasoning (...) supported by DIO one can distinguish both (1) basic reasoning about general structures in reality and (2) the domain-specific reasoning of experts. We here propose a clarification of this important distinction between (realist) reasoning on the basis of an ontology and rule-based inferences on the basis of an expert’s view. (shrink)

We introduce a framework that allows for the construction of sequent systems for expressive description logics extending ALC. Our framework not only covers a wide array of common description logics, but also allows for sequent systems to be obtained for extensions of description logics with special formulae that we call "role relational axioms." All sequent systems are sound, complete, and possess favorable properties such as height-preserving admissibility of common structural rules and height-preserving invertibility of rules.

1971. Discourse Grammars and the Structure of Mathematical Reasoning II: The Nature of a Correct Theory of Proof and Its Value, Journal of Structural Learning 3, #2, 1–16. REPRINTED 1976. Structural Learning II Issues and Approaches, ed. J. Scandura, Gordon & Breach Science Publishers, New York, MR56#15263. -/- This is the second of a series of three articles dealing with application of linguistics and logic to the study of mathematical reasoning, especially in the setting of a concern for improvement (...) of mathematical education. The present article presupposes the previous one. Herein we develop our ideas of the purposes of a theory of proof and the criterion of success to be applied to such theories. In addition we speculate at length concerning the specific kinds of uses to which a successful theory of proof may be put vis-a-vis improvement of various aspects of mathematical education. The final article will deal with the construction of such a theory. The 1st is the 1971. Discourse Grammars and the Structure of Mathematical Reasoning I: Mathematical Reasoning and Stratification of Language, Journal of Structural Learning 3, #1, 55–74. https://www.academia.edu/s/fb081b1886?source=link . (shrink)

This paper presents rules in sequent calculus for a binary quantifier I to formalise definite descriptions: Ix[F, G] means ‘The F is G’. The rules are suitable to be added to a system of positive free logic. The paper extends the proof of a cut elimination theorem for this system by Indrzejczak by proving the cases for the rules of I. There are also brief comparisons of the present approach to the more common one that formalises definite descriptions with a (...) term forming operator. In the final section rules for I for negative free and classical logic are also mentioned. (shrink)

In this paper we discuss a new perspective on the syntax-semantics interface. Semantics, in this new set-up, is not ‘read off’ from Logical Forms as in mainstream approaches to generative grammar. Nor is it assigned to syntactic proofs using a Curry-Howard correspondence as in versions of the Lambek Calculus, or read off from f-structures using Linear Logic as in Lexical-Functional Grammar (LFG, Kaplan & Bresnan [9]). All such approaches are based on the idea that syntactic objects (trees, proofs, fstructures) (...) are somehow prior and that semantics must be parasitic on those syntactic objects. We challenge this idea and develop a grammar in which syntax and semantics are treated in a strictly parallel fashion. The grammar will have many ideas in common with the (converging) frameworks of categorial grammar and LFG, but its treatment of the syntax-semantics interface is radically different. Also, although the meaning component of the grammar is a version of Montague semantics and although there are obvious affinities between Montague’s conception of grammar and the work presented here, the grammar is not compositional, in the sense that composition of meaning need not follow surface structure. (shrink)

Husserl’s Logical Grammar is intended to explain how complex expressions can be constructed out of simple ones so that their meaning turns out to be determined by the meanings of their constituent parts and the way they are put together. Meanings are thus understood as structured contents and classified into formal categories to the effect that the logical properties of expressions reflect their grammatical properties. As long as linguistic meaning reduces to the intentional content of pre-linguistic representations, however, (...) it is not trivial to account for how semantics relates to syntax in this context. In this paper, I analyze Husserl’s Logical Grammar as a system of recursive rules operating on representations and suggest that the syntactic form of representations contributes to their semantics because it carries information about semantic role. I further discuss Husserl’s syntactic account of the unity of propositions and argue that, on this account, logical form supervenes on syntactic form. In the last section I draw some implications for the phenomenology of thought and conjecture that the structural features it displays are likely to convey the syntactic structures of an underlying language-like representational system. (shrink)

This original research hypothesises that the most fundamental building blocks of logical descriptions of cognitive, or knowledge, agents’ descriptions are expressible based on their conceptions (of the world). This article conceptually and logically analyses agents’ conceptions in order to offer a constructivist- based logical model for terminological knowledge. The most significant characteristic of [terminological] knowing is that there are strong interrelationships between terminological knowledge and the individualistic constructed, and to-be-constructed, models of knowledge. Correspondingly, I conceptually and logically analyse (...) conception expressions based on terminological knowledge, and I show how terminological knowledge may reasonably be assumed to be constructed based on the agents’ conceptions of the world. The focus of my model is on terminological knowledge structures, which may find applications in such diverse fields as the Semantic Web and educational/learning systems. (shrink)

Rozprawa podkreśla związek między językową argumentacją a logiką. Argumentacja językowa jest systemem językowym, który stosuje znaczenie wyrażeń ujętych w zdania do zarysowania pełnego znaczenia zdań, w nich bowiem konstytuują się zależności między wyrażeniami. Rzeczywiście, to powiązanie między wyrażeniami wzmacnia całościowe znaczenie począwszy od samych podstaw struktury zdania w logicznym powiązaniu idei. W nim znajduje się relacja między słowami a umysłem, zależna od logiki powiązanych ze sobą wypowiedzi. Aby podkreślić znaczenie przedstawionego wyżej sposobu myślenia, autorka zwraca się ku teorii wczesnej gramatyki (...) arabskiej, ogniskującej się raczej wokół analogii niż anomalii. Nastawienie w systemie na analogię opiera się na podstawowej teorii, która implikuje wspomnianą wyżej relację, choć niektóre współczesne ujęcia odrzucają tę interpretację. W podsumowaniu swojej analizy, autorka uwzględnia podobne teorie gramatyki łacińskiej, które wykazują nastawienie logiczne, będące następstwem powiązania językowej argumentacji z logiką. Konkludując, autorka stwierdza, iż powiązanie słów i logiki okazuje się pojęciem uniwersalnym. (shrink)

I argue that the ability to compute phrase structure grammars is indicative of a particular kind of thought. This type of thought that is only available to cognitive systems that have access to the computations that allow the generation and interpretation of the structural descriptions of phrase structure grammars. The study of phrase structure grammars, and formal language theory in general, is thus indispensable to studies of human cognition, for it makes explicit both the unique type of (...) human thought and the underlying mechanisms in virtue of which this thought is made possible. (shrink)

Expressiveness and decidability are two core aspects of programming languages that should be thoroughly known by those who use them; this includes knowledge of their metalanguages a.k.a. formal grammars. The van Wijngaarden grammars (WGs) are capable of generating all the languages in the Chomsky hierarchy and beyond; this makes them a relevant tool in the design of (more) expressive programming languages. But this expressiveness comes at a very high cost: The syntax of WGs is extremely complex and the (...) decision problem for the generated languages is generally unsolvable. With this in mind, I provide here a short primer of the syntax of WGs, which includes syntactic restrictions that guarantee decidability for the corresponding generated languages. (shrink)

This paper introduces λ-grammar, a form of categorial grammar that has much in common with LFG. Like other forms of categorial grammar, λ-grammars are multi-dimensional and their components are combined in a strictly parallel fashion. Grammatical representations are combined with the help of linear combinators, closed pure λ-terms in which each abstractor binds exactly one variable. Mathematically this is equivalent to employing linear logic, in use in LFG for semantic composition, but the method seems more practicable.

Formalisms based on one or other flavor of Description Logic (DL) are sometimes put forward as helping to ensure that terminologies and controlled vocabularies comply with sound ontological principles. The objective of this paper is to study the degree to which one DL-based biomedical terminology (SNOMED CT) does indeed comply with such principles. We defined seven ontological principles (for example: each class must have at least one parent, each class must differ from its parent) and examined the properties of (...) SNOMED CT classes with respect to these principles. Our major results are: 31% of these classes have a single child; 27% have multiple parents; 51% do not exhibit any differentiae between the description of the parent and that of the child. The applications of this study to quality assurance for ontologies are discussed and suggestions are made for dealing with the phenomenon of multiple inheritance. The advantages and limitations of our approach are also discussed. (shrink)

In Pietroski ( 2018 ) a simple representation language called SMPL is introduced, construed as a hypothesis about core conceptual structure. The present work is a study of this system from a logical perspective. In addition to establishing a completeness result and a complexity characterization for reasoning in the system, we also pinpoint its expressive limits, in particular showing that the fourth corner in the square of opposition (“ Some_not ”) eludes expression. We then study a seemingly small extension, (...) called SMPL +, which allows for a minimal predicate-binding operator. Perhaps surprisingly, the resulting system is shown to encode precisely the concepts expressible in first-order logic. However, unlike the latter class, the class of SMPL + expressions admits a simple procedural (context-free) characterization. Our contribution brings together research strands in logic—including natural logic, modal logic, description logic, and hybrid logic—with recent advances in semantics and philosophy of language. (shrink)

In this study, I intend to show how and why, in the Port-Royal Logic, a singular term can reveal the nature of the logical judgment in the handbook. As I argue, the treatment given to one of thee singular terms, namely, the defined descriptions, in the terminology introduced by Russell, leads to an opening to langage that sounds unexpected and unjustified. Considering the privilege of thinking over langage and also that judgment is the mental act that defines logic, however, (...) we may understand how the authors regard langage, in relation to the epistemic constituents, namely, the mental acts within the terms. In doing so we are compelled to recognize the implications of this step towards pragmatism in fixing the meaning of defined descriptions to the nature of judgment in the handbook. This opening to langage reveals the conception of judgment as a twofold mental act: a formal and a practical (moral and theological) one. (shrink)

The label `semiotic grammar' captures a fundamental property of the grammars of human languages: not only is language a semiotic system in the familiar Saussurean sense, but its organizing system, its grammar, is also a semiotic system. This proposition, explicated in detail by William McGregor in this book, constitutes a new theory of grammar. Semiotic Grammar is `functional' rather than `formal' in its intellectual origins, approaches, and methods. It demonstrates, however, that neither a purely functional nor a purely formal (...) account of language is adequate, given the centrality of the sign as the fundamental unit of grammatical analysis. The author distinguishes four types of grammatical signs: experiential, logical, interpersonal, and textural. The signifiers of these signs are syntagmatic relationships of the following types, respectively: constituency, dependency, conjugational and linking. McGregor illustrates and exemplifies the theory with data from a variety of languages including English, Acehnese, Polish, Finnish, Japanese, Chinese, and Mohawk; and from his pioneering research on Gooniyandi and Nyulnyul, two languages of the Kimberleys region of Western Australia. (shrink)

In his new book, Logical Form, Andrea Iacona distinguishes between two different roles that have been ascribed to the notion of logical form: the logical role and the semantic role. These two roles entail a bifurcation of the notion of logical form. Both notions of logical form, according to Iacona, are descriptive, having to do with different features of natural language sentences. I agree that the notion of logical form bifurcates, but not that the (...) logical role is merely descriptive. In this paper, I focus on formalization, a process by which logical form, on its logical role, is attributed to natural language sentences. According to some, formalization is a form of explication, and it involves normative, pragmatic, as well as creative aspects. I present a view by which formalization involves explicit commitments on behalf of a reasoner or an interpreter, which serve the normative grounds for the evaluation of a given text. In previous work, I proposed the framework of semantic constraints for the explication of logical consequence. Here, I extend the framework to include formalization constraints. The various constraints then serve the role of commitments. I discuss specific issues raised by Iacona concerning univocality, co-reference and equivocation, and I show how our views on these matters diverge as a result of our different starting assumptions. (shrink)

In this work we present NERVOUS, an intelligent recommender system exploiting a probabilistic extension of a Description Logic of typicality to dynamically generate novel contents in AllMusic, a comprehensive and in-depth resource about music, providing data about albums, bands, musicians and songs. The tool can be used for both the generation of novel music genres and styles, described by a set of typical properties characterizing them, and the reclassification of the available songs within such new genres.

Recent work in formal semantics suggests that the language system includes not only a structure building device, as standardly assumed, but also a natural deductive system which can determine when expressions have trivial truth-conditions (e.g., are logically true/false) and mark them as unacceptable. This hypothesis, called the `logicality of language', accounts for many acceptability patterns, including systematic restrictions on the distribution of quantifiers. To deal with apparent counter-examples consisting of acceptable tautologies and contradictions, the logicality of language is often paired (...) with an additional assumption according to which logical forms are radically underspecified: i.e., the language system can see functional terms but is `blind' to open class terms to the extent that different tokens of the same term are treated as if independent. This conception of logical form has profound implications: it suggests an extreme version of the modularity of language, and can only be paired with non-classical---indeed quite exotic---kinds of deductive systems. The aim of this paper is to show that we can pair the logicality of language with a different and ultimately more traditional account of logical form. This framework accounts for the basic acceptability patterns which motivated the logicality of language, can explain why some tautologies and contradictions are acceptable, and makes better predictions in key cases. As a result, we can pursue versions of the logicality of language in frameworks compatible with the view that the language system is not radically modular vis-a-vis its open class terms and employs a deductive system that is basically classical. (shrink)

Cet article porte sur la notion de description (Beschreibung) chez Marty. L’article débute par l’étude de la distinction entre psychologie descriptive et génétique chez Brentano, non seulement dans les cours donnés à Vienne dès 1887, mais également dans la Psychologie du point de vue empirique. L’article se concentre ensuite sur la reprise martyienne de cette distinction. Si Marty, fidèle à la pensée de son maître, en reprend les principales conclusions dans ses propres travaux de psychologie, il étend de manière (...) originale la distinction entre recherches descriptives et génétiques à la philosophie du langage, notamment à la « sémasiologie » (Semasiologie) ou « théorie de la signification » (Bedeutungslehre). L’article se clôt sur une discussion des critiques adressées par Husserl à la philosophie du langage de Marty. (shrink)

ABSTRACT This part of the series has a dual purpose. In the first place we will discuss two kinds of theories of proof. The first kind will be called a theory of linear proof. The second has been called a theory of suppositional proof. The term "natural deduction" has often and correctly been used to refer to the second kind of theory, but I shall not do so here because many of the theories so-called are not of the second kind--they (...) must be thought of either as disguised linear theories or theories of a third kind (see postscript below). The second purpose of this part is 25 to develop some of the main ideas needed in constructing a comprehensive theory of proof. The reason for choosing the linear and suppositional theories for this purpose is because the linear theory includes only rules of a very simple nature, and the suppositional theory can be seen as the result of making the linear theory more comprehensive. CORRECTION: At the time these articles were written the word ‘proof’ especially in the phrase ‘proof from hypotheses’ was widely used to refer to what were earlier and are now called deductions. I ask your forgiveness. I have forgiven Church and Henkin who misled me. (shrink)

This paper raises some questions about the formalization of sentences containing ‘if’ or similar expressions. In particular, it focuses on three kinds of sentences that resemble conditionals in some respects but exhibit distinctive logical features that deserve separate consideration: whether-or-not sentences, biscuit conditionals, and concessive conditionals. As will be suggested, the examples discussed show in different ways that an adequate formalization of a sentence must take into account the content expressed by the sentence. This upshot is arguably what one (...) should expect on the view that logical form is determined by truth conditions. (shrink)