This paper maps out the relation between different approaches for handling preferences in argumentation with strict rules and defeasible assumptions by offering translations between them. The systems we compare are: non-prioritized defeats, preference-based defeats, and preference-based defeats extended with reverse defeat. We prove that these translations preserve the consequences of the respe...

In this paper we present an extension of the traditional approach to assumption-based reasoning. Instead of propositional logic we use the framework of finite set constraints. The idea is that a proposition x can also be considered as Boolean variable x ∈ {0, 1}. The literals x and ∼x are then represented by Boolean set constraints x ∈ {1} and x ∈ {0} respectively. More generally, arbitrary fin...

In this paper, we present two different formal frameworks for representing decision making. In both frameworks, decisions have multiple attributes and meet different goals. In the second framework, decisions take into account preferences over goals. We also study a family of decision functions representing making decisions with different criteria, including decisions meeting all goals, most goa...

We introduce NDL, a new formalization of Fitch-style natural deduction based on the abstraction of assumption bases. NDL proofs tend to be readable, writable, concise, and can be checked very efficiently. We present the abstract syntax of NDL, followed by two different kinds of formal semantics: evaluation and denotational. We then relate the two semantics and show how proof checking becomes ta...

Let K denote a field and let V denote a vector space over K with finite positive dimension. We consider a pair of linear transformations A : V → V and A∗ : V → V that satisfy the following conditions: (i) each of A,A∗ is diagonalizable; (ii) there exists an ordering {Vi} d i=0 of the eigenspaces of A such that A ∗Vi ⊆ Vi−1+Vi+Vi+1 for 0 ≤ i ≤ d, where V−1 = 0 and Vd+1 = 0; (iii) there exists an...

The identification of average causal effects of a treatment in observational studies is typically based either on the unconfoundedness assumption (exogeneity of the treatment) or on the availability of an instrument. When available, instruments may also be used to test for the unconfoundedness assumption. In this paper, we present a set of assumptions on an instrumental variable which allows us...

CD0-type spaces were firstly introduced by Yu. A. Abramovich and A. W. Wickstead in [1] and [2] and further investigated by S. Alpay and Z. Ercan in [3]. CD0-type spaces deserve to be called Abramovich–Wickstead spaces, or briefly AW -space as in [4], since they mainly stem from the works of Yu. A. Abramovich and A. W. Wickstead. In this note we construct a new type AW -space and call it CDr 0 ...