Download An Introduction to Symbolic Logic and Its Applications by Rudolf Carnap PDF

By Rudolf Carnap

A transparent, entire, and rigorous therapy develops the topic from undemanding techniques to the development and research of particularly advanced logical languages. It then considers the appliance of symbolic good judgment to the rationalization and axiomatization of theories in arithmetic, physics, and biology. 1000s of difficulties, examples, and workouts. 1958 variation.

Show description

Read or Download An Introduction to Symbolic Logic and Its Applications PDF

Best logic books

An Introduction to Symbolic Logic and Its Applications

A transparent, finished, and rigorous therapy develops the topic from common strategies to the development and research of fairly advanced logical languages. It then considers the appliance of symbolic common sense to the rationalization and axiomatization of theories in arithmetic, physics, and biology.

Errors of Reasoning. Naturalizing the Logic of Inference

Blunders of Reasoning is the long-awaited continuation of the author's research of the good judgment of cognitive platforms. the current concentration is the person human reasoner working below the stipulations and pressures of actual lifestyles with capacities and assets the wildlife makes to be had to him.

Quanta, logic and spacetime

During this increased variation of Quanta, common sense and Spacetime, the logical base is enormously broadened and quantum-computational facets of the strategy are delivered to the fore. the 1st elements of this variation could certainly be considered as delivering a self-contained and logic-based beginning for — and an advent to — the company often called quantum computing.

Knowledge Representation and Reasoning Under Uncertainty: Logic at Work

This quantity relies at the foreign convention good judgment at paintings, held in Amsterdam, The Netherlands, in December 1992. The 14 papers during this quantity are chosen from 86 submissions and eight invited contributions and are all dedicated to wisdom illustration and reasoning less than uncertainty, that are middle problems with formal synthetic intelligence.

Extra info for An Introduction to Symbolic Logic and Its Applications

Example text

Hence -f(-x) I -fA(-x). By the general rule that f(x) If(y) follows from x Iy, which holds in all extensions of K, we conclude that f(-f( -x)) I f(-fA( -x)). fA(-fA(-x)) is the union of all elements in BA below f(-fA(-x)). One of these is evidently x. Hence x 5 fA( -fA( -x)). In our framework, generalizations to many-place operators is quite straightforward and our theorem will work as before. As a simple example we take the following system QP of qualitative probability with the two-place operator (to be interpreted as ‘as least as probable as’).

Unc Chd+e) ( y , P ) , ... (17) It is easily seen that if the last layer of quantifiers is omitted from result is either identical with (16) or can be obtained from it by omitting some attributive constituents. This simply reflects the fact that one’s uncertainty about P grows smaller when a new layer of quantifiers is admitted to the description of individuals in terms of the defining constants pl. Thus each branch of (16) is either continued or cut off in Unc CAd+e+l) 6% PI. What are now the most important things that can happen in (17) and what do they tell us about the dehability of P in the complete theory (l)?

D) Finite ident$ubility [12]. , x,J disappear that are derived from ‘indistinguishable’ (in v) constituents C(d+e - k) (9,p , x1 xk) 9 occurring as (not necessarily consecutive) parts of the constituent CAd+e) of (1) at which the disappearance takes place. Two such constituents Cd (9,p , x1, . *> xk), c, Y * * . ,Xk) are identical. ) 54 JAAKKO HINTIKKA A N D VEIKKO RANTALA occurs as a part of (tp, P ) means that occurs there as a consecutive part and that the + B , , fB, , ... (with the appropriate ‘signs’) occur there with their variables bound to the same quantifiers as the variables of CtY+e-k , ( 9 ) , p , x l ,.

Download PDF sample

Rated 4.36 of 5 – based on 37 votes