Equality-free Logic: The Method of Diagrams and Preservation Theorems
نویسنده
چکیده
In this article I prove preservation theorems for the positive and for the universal-existential fragment of equality-free logic. I give a systematic presentation of the method of diagrams for first-order languages without equality.
منابع مشابه
Preservation theorems in {L}ukasiewicz \model theory
We present some model theoretic results for {L}ukasiewiczpredicate logic by using the methods of continuous model theorydeveloped by Chang and Keisler.We prove compactness theorem with respect to the class of allstructures taking values in the {L}ukasiewicz $texttt{BL}$-algebra.We also prove some appropriate preservation theorems concerning universal and inductive theories.Finally, Skolemizatio...
متن کاملEquality propositional logic and its extensions
We introduce a new formal logic, called equality propositional logic. It has two basic connectives, $boldsymbol{wedge}$ (conjunction) and $equiv$ (equivalence). Moreover, the $Rightarrow$ (implication) connective can be derived as $ARightarrow B:=(Aboldsymbol{wedge}B)equiv A$. We formulate the equality propositional logic and demonstrate that the resulting logic has reasonable properties such a...
متن کاملOn Elementary Equivalence for Equality-free Logic
This paper is a contribution to the study of equality-free logic, that is, first-order logic without equality. We mainly devote ourselves to the study of algebraic characterizations of its relation of elementary equivalence by providing some Keisler-Shelah type ultrapower theorems and an Ehrenfeucht-Fraı̈ssé type theorem. We also give characterizations of elementary classes in equalityfree logic...
متن کاملA rule-based evaluation of ladder logic diagram and timed petri nets for programmable logic controllers
This paper describes an evaluation through a case study by measuring a rule-based approach, which proposed for ladder logic diagrams and Petri nets. In the beginning, programmable logic controllers were widely designed by ladder logic diagrams. When complexity and functionality of manufacturing systems increases, developing their software is becoming more difficult. Thus, Petri nets as a high l...
متن کاملOn the expressiveness of spider diagrams and commutative star-free regular languages
Spider diagrams provide a visual logic to express relations between sets and their elements, extending the expressiveness of Venn diagrams. Sound and complete inference systems for spider diagrams have been developed and it is known that they are equivalent in expressive power to monadic first-order logic with equality, MFOL[1⁄4]. languages that are finite unions of languages of the form K G , ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- Logic Journal of the IGPL
دوره 7 شماره
صفحات -
تاریخ انتشار 1999