scholarly journals Predicate Logic with Anaphora

1994 ◽  
Vol 4 ◽  
pp. 79 ◽  
Author(s):  
Paul Dekker
Keyword(s):  
Type Theory ◽  
Predicate Logic ◽  
Discourse Representation ◽  
Dynamic Predicate Logic ◽  
Proper Extension ◽  
Update Semantics ◽  
Anaphoric Pronouns ◽  
Separate Treatment

In this paper I make a case for a separate treatment of (singular) anaphoric pronouns within a predicate logic with anaphora (PLA). Discourse representation theoretic results (from Kamp 1981) can be formulated in a compositional way, without fid­dling with orthodox notions of scope and binding. In contrast with its predecessor dynamic predicate logic (Groenendijk and Stokhof 1991), the system of PLA is a proper extension of ordinary predicate logic and it has a genuine update semantics. Moreover, in contrast with other compositional reformulations of DRT, the seman­tics of PLA remains well within the bounds of ordinary, extensional type theory.

Predicate Logic with Anaphora

2015 ◽  
pp. 79
Author(s):  
Paul Dekker
Keyword(s):  
Type Theory ◽  
Predicate Logic ◽  
Discourse Representation ◽  
Dynamic Predicate Logic ◽  
Proper Extension ◽  
Update Semantics ◽  
Anaphoric Pronouns ◽  
Separate Treatment

In this paper I make a case for a separate treatment of (singular) anaphoric pronouns within a predicate logic with anaphora (PLA). Discourse representation theoretic results (from Kamp 1981) can be formulated in a compositional way, without fid­dling with orthodox notions of scope and binding. In contrast with its predecessor dynamic predicate logic (Groenendijk and Stokhof 1991), the system of PLA is a proper extension of ordinary predicate logic and it has a genuine update semantics. Moreover, in contrast with other compositional reformulations of DRT, the seman­tics of PLA remains well within the bounds of ordinary, extensional type theory.

Type-logical semantics

2018 ◽  
Author(s):  
Reinhard Muskens
Keyword(s):  
Type Theory ◽  
Predicate Logic ◽  
Logical Form ◽  
Ordinary Language ◽  
Linguistic Meaning ◽  
Lexical Meaning ◽  
Logical Language ◽  
Competing Hypotheses ◽  
Richard Montague ◽  
Logical Semantics

Type-logical semantics studies linguistic meaning with the help of the theory of types. The latter originated with Russell as an answer to the paradoxes, but has the additional virtue that it is very close to ordinary language. In fact, type theory is so much more similar to language than predicate logic is, that adopting it as a vehicle of representation can overcome the mismatches between grammatical form and predicate logical form that were observed by Frege and Russell. The grammatical forms of ordinary language sentences consequently may be taken to be much less misleading than logicians in the first half of the twentieth century often thought them to be. This was realized by Richard Montague, who used the theory of types to translate fragments of ordinary language into a logical language. Semantics is commonly divided into lexical semantics, which studies the meaning of words, and compositional semantics, which studies the way in which complex phrases obtain a meaning from their constituents. The strength of type-logical semantics lies with the latter, but type-logical theories can be combined with many competing hypotheses about lexical meaning, provided these hypotheses are expressed using the language of type theory.

scholarly journals Evidentiality and temporal distance learning

2011 ◽  
Vol 21 ◽  
pp. 115 ◽  
Author(s):  
Todor Koev
Keyword(s):  
Distance Learning ◽  
Predicate Logic ◽  
Temporal Distance ◽  
Grammatical Category ◽  
Dynamic Predicate Logic ◽  
Evidence Type ◽  
Topic Time

The grammatical category of evidentiality is traditionally defined as marking evidence type or related concepts (Anderson 1986, Willett 1988, Aikhenvald 2004). I argue against this received view as I show that evidential morphemes in Bulgarian mark the temporal distance between the time at which the speaker learned the described proposition and the topic time. I also demonstrate that Bulgarian evidentials represent projective/backgrounded content that is informative but does not affect the described proposition, which is plainly entailed. The latter fact especially has important typological and theoretical consequences. The proposal is formalized in a logic that extends Dynamic Predicate Logic by adding propositional variables (cf. AnderBois et al. 2010).

Martin-Löf ’s type theory

2001 ◽  
Author(s):  
B. Nördstrom ◽  
K. Petersson
Keyword(s):  
Computer Program ◽  
Programming Language ◽  
Type Theory ◽  
Predicate Logic ◽  
Propositional Calculus ◽  
Constructive Proof ◽  
Intuitionistic Propositional Calculus ◽  
Problem Description ◽  
Program Construction ◽  
Correct Program

The type theory described in this chapter has been developed by Martin-Löf with the original aim of being a clarification of constructive mathematics. Unlike most other formalizations of mathematics, type theory is not based on predicate logic. Instead, the logical constants are interpreted within type theory through the Curry-Howard correspondence between propositions and sets [Curry and Feys, 1958; Howard, 1980]: a proposition is interpreted as a set whose elements represent the proofs of the proposition. It is also possible to view a set as a problem description in a way similar to Kolmogorov’s explanation of the intuitionistic propositional calculus [Kolmogorov, 1932]. In particular, a set can be seen as a specification of a programming problem; the elements of the set are then the programs that satisfy the specification. An advantage of using type theory for program construction is that it is possible to express both specifications and programs within the same formalism. Furthermore, the proof rules can be used to derive a correct program from a specification as well as to verify that a given program has a certain property. As a programming language, type theory is similar to typed functional languages such as ML [Gordon et al., 1979; Milner et al., 1990] and Haskell [Hudak et al, 1992], but a major difference is that the evaluation of a well-typed program always terminates. The notion of constructive proof is closely related to the notion of computer program. To prove a proposition ("x Î A)($yÎB)P(x,y) constructively means to give a function f which when applied to an element a in A gives an element b in B such that P(a, b) holds. So if the proposition ("xÎ A)($yÎB)P(x,y) expresses a specification, then the function f obtained from the proof is a program satisfying the specification. A constructive proof could therefore itself be seen as a computer program and the process of computing the value of a program corresponds to the process of normalizing a proof. It is by this computational content of a constructive proof that type theory can be used as a programming language; and since the program is obtained from a proof of its specification, type theory can be used as a programming logic.

An intensional type theory: motivation and cut-elimination

2001 ◽  
Vol 66 (1) ◽  
pp. 383-400 ◽  
Author(s):  
Paul C Gilmore
Keyword(s):  
Type Theory ◽  
Proof Theory ◽  
Predicate Logic ◽  
Order Term ◽  
Higher Order ◽  
Cut Elimination ◽  
Consistency Proof ◽  
Completeness Proof ◽  
Higher Order Term

AbstractBy the theory TT is meant the higher order predicate logic with the following recursively defined types:(1) 1 is the type of individuals and [] is the type of the truth values:(2) [τ1…..τn] is the type of the predicates with arguments of the types τ1…..τn.The theory ITT described in this paper is an intensional version of TT. The types of ITT are the same as the types of TT, but the membership of the type 1 of individuals in ITT is an extension of the membership in TT. The extension consists of allowing any higher order term, in which only variables of type 1 have a free occurrence, to be a term of type 1. This feature of ITT is motivated by a nominalist interpretation of higher order predication.In ITT both well-founded and non-well-founded recursive predicates can be defined as abstraction terms from which all the properties of the predicates can be derived without the use of non-logical axioms.The elementary syntax, semantics, and proof theory for ITT are defined. A semantic consistency proof for ITT is provided and the completeness proof of Takahashi and Prawitz for a version of TT without cut is adapted for ITT: a consequence is the redundancy of cut.

scholarly journals Ambiguity and Anaphora with Plurals in Discourse

2015 ◽  
pp. 19
Author(s):  
Nicholas Asher ◽  
Linton Wang
Keyword(s):  
Lexical Semantics ◽  
Predicate Logic ◽  
Dynamic Semantics ◽  
Dynamic Predicate Logic ◽  
Different Types ◽  
Left And Right ◽  
Dynamic Transitions ◽  
Inputs And Outputs

We provide examples of plurals related to ambiguity and anaphora that pose problems or are counterexamples for current approaches to plurals. We then propose a dynamic semantics based on an extension of dynamic predicate logic (DPL<sup>+</sup>) to handle these examples. On our theory, different readings of sentences or discourses containing plu­rals don't arise from a postulated ambiguity of plural terms or predicates applying to plural DPs, but follow rather from different types of dynamic transitions that manip­ulate inputs and outputs from formulas or discourse constituents. Many aspects of meaning can affect the type dynamic transitions : the lexical semantics of predicates to the left and right of a transition, and number features of DPs and discourse constraints like parallelism.

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