Predicate logic unplugged

this paper we describe the syntax and semantics of a description language for underspecified semantic representations. This concept is discussed in general and in particular applied to Predicate Logic and Discourse Representation Theory. The reason for exploring underspecified representations as suitable semantic representations for natural language expressions emerges directly from practical natural language processing applications. The so-called Combinatorial Explosion Puzzle, a well known problem in this area, can succesfully be tackled by using underspecified representations. The source of this problem, scopal ambiguities in natural language expressions, is discussed in section 2. The core of the paper presents Hole Semantics. This is a general proposal for a framework, in principle suitable for any logic, where underspecified representations play a central role. There is a clear separation between the object language (the logical language one is interested in) and the meta language (the language that describes and interprets underspecified structures). It has been noted by various authors that the meaning of an underspecified semantic representation cannot be expressed in terms of a disjunction of denotations, but rather as a set of denotations (cf. Poesio 1994). We support this view, and use it as underlying principle for the definition of the semantic interpretation function of underspecified structures. Section 3 is an informal introduction to Hole Semantics, and in section 4 things are formally defined. In section 5 we apply Hole Semantics to Predicate Logic, resulting in an "unplugged" version of (static and dynamic) Predicate Logic. In section 6 we show that this idea easily carries over to Discourse Representation Structures. A lot of attention has been paid..

Ambiguity and reasoning

In this paper, reasoning with ambiguous representations is explored in a formal way, with ambiguities at the level of propositions in propositional logic and predicate logic, and ambiguous representations of scopings in predicate logic as the main examples. First a version of propositional logic with propositional ambiguities is presented and a sequent axiomatization for it is given. This is then extended to predicate logic. Next, predicate logic with scope ambiguities is introduced and discussed, and again a sequent calculus for it is proposed. The conclusion connects the results to natural language semantics, and briefly compares them with existing logics of ambiguity. An appendix gives completeness proofs for our versions of ambiguous propositional and predicate logic

Hubungan Antara Logika Proposisi Dengan Logika Predikat (Suatu Kajian Epistemologis)

This paper presents epistemological studies of propositional logic and predicate logic. The topic is a part of the dissertation proposal under title “Ëpistemology of Mathematical Logic According to Ludwig Wittgenstein”. Author is a student of the Doctor Program of Gajah Mada University, the majorstudy is philosophy. There are some difference, equality, and relation between propositional logic and predicate logic. Both of them use the same ope-rator, method, and rule of inference. There are five operator of logic, that are disjunction, conjunction, negation, implication, and biimplication. The truth value of proposition deter-minated by definition. There are eighteen rules of inference, four rules for removing quan-tifiers, and four rules for introducing quantifiers. There are two methods of validity test, that are direct proof and indirect proof; and there is one common method for invalidity test , that is Counter Exampel Method. The basic component of propositional logic is simple statement. The basic component of predicate logic is predicate. In the predicate logic beside Counter Exampel Method for invalidity test, there is another method for invalidity test that is Finite Universe Method. The conclusion of this research is propositional logic which a part of predicate logic. If a form is valid in propositional logic, then the form is valid in predicate logics. Thus scope of predicate logic is wider than propositional logic

Formalizing Self-Reference Paradox using Predicate Logic

We begin with the hypothetical assumption that Tarski’s 1933 formula ∀ True(x) φ(x) has been defined such that ∀x Tarski:True(x) ↔ Boolean-True. On the basis of this logical premise we formalize the Truth Teller Paradox: "This sentence is true." showing syntactically how self-reference paradox is semantically ungrounded

Delimited control operators prove Double-negation Shift

We propose an extension of minimal intuitionistic predicate logic, based on delimited control operators, that can derive the predicate-logic version of the Double-negation Shift schema, while preserving the disjunction and existence properties