We give semantic characterizations for the notions of reachability and trace equivalence in a linear-logic based framework of asyncronous concurrent process calculus. Usually the reachability relation in linear logic-based concurrent process calculi is characterized by the logical notion of provability, which is in turn characterized by model-theoretic semantics such as the phase semantics. The...

We introduce a unified logical approach, based on signed theories and Quantified Boolean Formulas (QBFs), that can serve as a basis for representing and reasoning with various argumentation-based decision problems. By this, we are able to represent, in a uniform and simple way, a wide range of extension-based semantics for argumentation theory, including complete, grounded, preferred, semistabl...

Rough set theory can be considered as the foundation of various kinds of deductive reasoning. In this paper, the authors do some logical investigations about the possibility of using partial approximation of sets as semantics of a three-valued partial logic which use one-argument predicate parameters without quantification. As a consequence of using the lower and upper approximation of sets, ap...

Fixpoints play a key role in the mathematical set up of abstract argumentation theory but, we argue, have been relatively underexamined in the literature. The paper studies the logical structure underlying the computation via approximation sequences of the sort of fixpoints relevant in argumentation. Concretely, it presents a number of novel results on the fixed point theory underpinning the ma...

In this paper we introduce a new logical foundation of SAND attack trees in intuitionistic linear logic. This new foundation is based on a new logic called the Attack Tree Linear Logic (ATLL). Before introducing ATLL we given several new logical models of attack trees, the first, is a very basic model based in truth tables. Then we lift this semantics into a semantics of attack trees based on l...

We introduce logical formalisms of production and causal inference relations based on input/output logics of [Makinson and van der Torre, 2000]. These inference relations are assigned, however, both standard monotonic semantics, and natural nonmonotonic semantics based on the principle of explanatory closure. The resulting nonmonotonic formalisms will be shown to provide a logical representatio...

The different semantics that can be assigned to a logic program correspond to different assumptions made concerning the atoms whose logical values cannot be inferred from the rules. Thus, the well founded semantics corresponds to the assumption that every such atom is false, while the Kripke-Kleene semantics corresponds to the assumption that every such atom is unknown. In this paper, we propos...

This paper shows how Z can be used as a substrate for an architectural style description language. The language provides a collection of abstract software types that support the description of execution and interface semantics, logical views, and relationships between logical views. The software types correspond to application-invariant Z schemas, which provide a type-theoretic basis for the la...

Abstract Complex reasoning problems are most clearly and easily specified using logical rules, but require recursive rules with aggregation such as count sum for practical applications. Unfortunately, the meaning of has been a significant challenge, leading to many disagreeing semantics. This paper describes unified semantics aggregation, extending founded constraint negation. The key idea is s...