Applications of Intuitionistic Logic in Answer Set Programming

We present some applications of intermediate logics in the field of Answer Set Programming (ASP). A brief, but comprehensive introduction to the answer set semantics, intuitionistic and other intermediate logics is given. Some equivalence notions and their applications are discussed. Some results on intermediate logics are shown, and applied later to prove properties of answer sets. A characterization of answer sets for logic programs with nested expressions is provided in terms of intuitionistic provability, generalizing a recent result given by Pearce. It is known that the answer set semantics for logic programs with nested expressions may select non-minimal models. Minimal models can be very important in some applications, therefore we studied them; in particular we obtain a characterization, in terms of intuitionistic logic, of answer sets which are also minimal models. We show that the logic G3 characterizes the notion of strong equivalence between programs under the semantic induced by these models. Finally we discuss possible applications and consequences of our results. They clearly state interesting links between ASP and intermediate logics, which might bring research in these two areas together.Comment: 30 pages, Under consideration for publication in Theory and Practice of Logic Programmin

Adverbial clauses with -ig and the “until -puzzle”

This paper is devoted to untangling some of the cross-linguistic puzzles that are associated with temporal adverbial clauses in general, and until-clauses in particular. After a brief introduction to the issues raised by the construction in Hungarian, the paper presents an overview of the complexities of until-clauses and prior attempts at analyzing these. Then, an account that was first proposed in MacDonald & Ürögdi (2009a;b; 2011) for English is presented, and it is argued that until-constructions do not require any of the special machinery that has been proposed to explain their behavior. The analysis outlined accounts for the properties of temporal adverbials formed withuntil andfor without reference to auxiliary concepts like “expletive negation” and “stativizing negation”. After this detour into English, we return to Hungarian, where until-clauses present a more complex picture than they do in Germanic, and we see how even these data can be accounted for without special stipulations. Finally, the results are tied into the general picture of temporal and event relativization (cf. Haegeman & Ürögdi 2010a;b), providing support for an analysis of a well-defined class of subordinate clauses involving operator movement

Reasoning about Minimal Belief and Negation as Failure

We investigate the problem of reasoning in the propositional fragment of MBNF, the logic of minimal belief and negation as failure introduced by Lifschitz, which can be considered as a unifying framework for several nonmonotonic formalisms, including default logic, autoepistemic logic, circumscription, epistemic queries, and logic programming. We characterize the complexity and provide algorithms for reasoning in propositional MBNF. In particular, we show that entailment in propositional MBNF lies at the third level of the polynomial hierarchy, hence it is harder than reasoning in all the above mentioned propositional formalisms for nonmonotonic reasoning. We also prove the exact correspondence between negation as failure in MBNF and negative introspection in Moore's autoepistemic logic

Embedding Non-Ground Logic Programs into Autoepistemic Logic for Knowledge Base Combination

In the context of the Semantic Web, several approaches to the combination of ontologies, given in terms of theories of classical first-order logic and rule bases, have been proposed. They either cast rules into classical logic or limit the interaction between rules and ontologies. Autoepistemic logic (AEL) is an attractive formalism which allows to overcome these limitations, by serving as a uniform host language to embed ontologies and nonmonotonic logic programs into it. For the latter, so far only the propositional setting has been considered. In this paper, we present three embeddings of normal and three embeddings of disjunctive non-ground logic programs under the stable model semantics into first-order AEL. While the embeddings all correspond with respect to objective ground atoms, differences arise when considering non-atomic formulas and combinations with first-order theories. We compare the embeddings with respect to stable expansions and autoepistemic consequences, considering the embeddings by themselves, as well as combinations with classical theories. Our results reveal differences and correspondences of the embeddings and provide useful guidance in the choice of a particular embedding for knowledge combination.Comment: 52 pages, submitte

Integration of Action and Language Knowledge: A Roadmap for Developmental Robotics

“This material is presented to ensure timely dissemination of scholarly and technical work. Copyright and all rights therein are retained by authors or by other copyright holders. All persons copying this information are expected to adhere to the terms and constraints invoked by each author's copyright. In most cases, these works may not be reposted without the explicit permission of the copyright holder." “Copyright IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE.”This position paper proposes that the study of embodied cognitive agents, such as humanoid robots, can advance our understanding of the cognitive development of complex sensorimotor, linguistic, and social learning skills. This in turn will benefit the design of cognitive robots capable of learning to handle and manipulate objects and tools autonomously, to cooperate and communicate with other robots and humans, and to adapt their abilities to changing internal, environmental, and social conditions. Four key areas of research challenges are discussed, specifically for the issues related to the understanding of: 1) how agents learn and represent compositional actions; 2) how agents learn and represent compositional lexica; 3) the dynamics of social interaction and learning; and 4) how compositional action and language representations are integrated to bootstrap the cognitive system. The review of specific issues and progress in these areas is then translated into a practical roadmap based on a series of milestones. These milestones provide a possible set of cognitive robotics goals and test scenarios, thus acting as a research roadmap for future work on cognitive developmental robotics.Peer reviewe

Clause union and verb raising phenomena in German

In this paper we discuss a class of constructions in German syntax which have been known as coherent infinitive, clause union or verb raising constructions. These data run against the predictions of strictly configurational theories by apparently having a syntactic structure where the subcategorization frames of two or more verbal heads are merged into one. Thus, in addition to a fully bi-clausal structure with two clearly separated verbal heads, we also have to envisage the case where a verb is apparently raised from an embedded to form a verb cluster together with its governing verb, while the sets of their arguments are merged into a single set, representing the case of clause union. In addition, there are constructions where there is no evidence for clause union, but where one could nevertheless argue for the formation of a verb cluster. We investigate these data by looking at a series of constructions which bear evidence on the issue. Among these are extraposition, which appears a reliable test for nonobligatory verb raising; subjectless constructions, which are possible only as the complements of so-called raising verbs but not of control verbs; S-pronominalization, which seems to be limited to equi-verbs; scrambling and long reflexivization, which we can take as evidence for clause union; the scope of adjuncts and negation which argues in favour of verb raising, but does not necessarily presuppose clause union; and finally certain topicalization phenomena which appear to violate almost any of the generalizations set up so far by configurational theories

On the Merits and Limits of Replication and Negation for IS Research

A simple idea underpins the scientific process: All results should be subject to continued testing and questioning. Given the particularities of our international IS discipline, different viewpoints seem to be required to develop a picture of the merits and limits of testing and replication. Hence, the authors of this paper approach the topic from different perspectives. Following the ongoing discourse in neighbouring disciplines, we start by highlighting the significance of testing, replication and negation for scientific discourse as well as for the sponsors of research initiatives. Next, we discuss types of replication research and the challenges associated with each. In the third section, challenging questions are raised in the light of the ability of IS research for self-correction. Then, we address publication issues related to types of replications that require shifting editorial behaviors. The fifth section reflects on the possible use and interpretation of replication results in the light of contingency. As a key takeaway, the paper suggests ways to identify studies worth replicating in our field and reflects on possible roles of replication and testing for future IS research