# -*- coding: utf-8 -*- 
import sys
from PyQt4 import QtCore, QtGui

class MainWindow(QtGui.QMainWindow):
    def __init__(self, parent = None):
        QtGui.QMainWindow.__init__(self, parent)
        
        OutButton = QtGui.QPushButton('-', self)
#        self.connect(OutButton, QtCore.SIGNAL('clicked()'),<!--выполнение метода method1 класса Logic--!> )

class Logic():
    a=2
    def method1(self):
        a+=a

if __name__ == "__main__":
    app = QtGui.QApplication(sys.argv)
    window = MainWindow()
    window.show()
        
    o=Logic()

#    window.OutButton.connect(window.OutButton, o.method1())
    sys.exit(app.exec_())

window = MainWindow()
o = Logic()
func = o.method1
window.connect(window.OutButton, QtCore.SIGNAL('clicked()'), func)
window.show()

# -*- coding: utf-8 -*-
import sys
from PyQt4.QtGui import *
from PyQt4.QtCore import *

class MainWindow(QMainWindow):
    def __init__(self, parent = None):
        QMainWindow.__init__(self, parent)
        outButton = QPushButton('outButton', self)
        self.o=Logic()  # self.o - атрибут MainWidow
        self.connect(outButton, SIGNAL('clicked()'), self.o.method1 )   # соединяемся с self.o.method1

class Logic():
    a=2  # a - атрибут класса Logic
    def method1(self):
          self.a += self.a  # поэтому обращение self.a
          print self.a

if __name__ == "__main__":
    app = QApplication(sys.argv)
    window=MainWindow()
    window.show()
    sys.exit(app.exec_())

# -*- coding: utf-8 -*-
import sys
from PyQt4.QtGui import *
from PyQt4.QtCore import *

class Logic():
    a=2
    def method1(self):
          self.a += self.a
          print self.a

if __name__ == "__main__":
    app = QApplication(sys.argv)
    button=QPushButton('pushButton')
    o=Logic()
    QObject.connect(button, SIGNAL('clicked()'),o.method1 )
    button.show()
    sys.exit(app.exec_())