Related papers: Range-based argumentation semantics as 2-valued mo…
Large Language Models (LLMs) excel at linear reasoning tasks but remain underexplored on non-linear structures such as those found in natural debates, which are best expressed as argument graphs. We evaluate whether LLMs can approximate…
In the last years, abstract argumentation has met with great success in AI, since it has served to capture several non-monotonic logics for AI. Relations between argumentation framework (AF) semantics and logic programming ones are…
Logic rules and inference are fundamental in computer science and have been studied extensively. However, prior semantics of logic languages can have subtle implications and can disagree significantly, on even very simple programs,…
In this paper, we introduce a new family of argument-ranking semantics which can be seen as a refinement of the classification of arguments into skeptically accepted, credulously accepted and rejected. To this end we use so-called social…
In this paper, we present an approach to define the semantics for object-oriented modeling languages. One important property of this semantics is to support underspecified and incomplete models. To this end, semantics is given as predicates…
We endow prioritised default logic (PDL) with argumentation semantics using the ASPIC+ framework for structured argumentation, and prove that the conclusions of the justified arguments are exactly the prioritised default extensions.…
We analyse the expressiveness of the two-valued semantics of abstract argumentation frameworks, normal logic programs and abstract dialectical frameworks. By expressiveness we mean the ability to encode a desired set of two-valued…
Part of the theory of logic programming and nonmonotonic reasoning concerns the study of fixed-point semantics for these paradigms. Several different semantics have been proposed during the last two decades, and some have been more…
In the Declarative Networking paradigm, Datalog-like languages are used to express distributed computations. Whereas recently formal operational semantics for these languages have been developed, a corresponding declarative semantics has…
Futrell and Mahowald (2025) frame the success of neural language models (LMs) as supporting gradient, usage-based linguistic theories. I argue that LMs can also instantiate theories based on formal structures - the types of theories seen in…
This paper introduces the notion of value-based argumentation frameworks, an extension of the standard argumentation frameworks proposed by Dung, which are able toshow how rational decision is possible in cases where arguments derive their…
Argumentation problems are concerned with determining the acceptability of a set of arguments from their relational structure. When the available information is uncertain, probabilistic argumentation frameworks provide modelling tools to…
We characterize the languages in the individual levels of the quantifier alternation hierarchy of first-order logic with two variables by identities. This implies decidability of the individual levels. More generally we show that the…
Argumentation has proved a useful tool in defining formal semantics for assumption-based reasoning by viewing a proof as a process in which proponents and opponents attack each others arguments by undercuts (attack to an argument's premise)…
We obtain, for the first time, a modular many-valued semantics for combined logics, which is built directly from many-valued semantics for the logics being combined, by means of suitable universal operations over partial non-deterministic…
Logic has proved essential for formally modeling software based systems. Such formal descriptions, frequently called specifications, have served not only as requirements documentation and formalisation, but also for providing the…
We propose a novel framework seamlessly providing key properties of both neural nets (learning) and symbolic logic (knowledge and reasoning). Every neuron has a meaning as a component of a formula in a weighted real-valued logic, yielding a…
We propose a categorial grammar based on classical multiplicative linear logic. This can be seen as an extension of abstract categorial grammars (ACG) and is at least as expressive. However, constituents of {\it linear logic grammars (LLG)}…
In this paper we reexamine the place and role of stable model semantics in logic programming and contrast it with a least Herbrand model approach to Horn programs. We demonstrate that inherent features of stable model semantics naturally…
A new class of integrable mappings and chains is introduced. Corresponding $(1+2)$ integrable systems invariant with respect to such discrete transformations are presented in an explicit form. Their soliton-type solutions are constructed in…