In this paper, we introduce an alternative approach to Temporal Answer Set Programming that relies on a variation of Temporal Equilibrium Logic (TEL) for finite traces. This approach allows us to even out the expressiveness of TEL over infinite traces with the computational capacity of (incremental) Answer Set Programming (ASP). Also, we argue that finite traces are more natural when reasoning about action and change. As a result, our approach is readily implementable via multi-shot ASP systems and benefits from an extension of ASP's full-fledged input language with temporal operators. This includes future as well as past operators whose combination offers a rich temporal modeling language. For computation, we identify the class of temporal logic programs and prove that it constitutes a normal form for our approach. Finally, we outline two implementations, a generic one and an extension of the ASP system clingo.

We describe an application of Answer Set Programming to the understanding of narratives about stereotypical activities, demonstrated via question answering. Substantial work in this direction was done by Erik Mueller, who modeled stereotypical activities as scripts. His systems were able to understand a good number of narratives, but could not process texts describing exceptional scenarios. We propose addressing this problem by using a theory of intentions developed by Blount, Gelfond, and Balduccini. We present a methodology in which we substitute scripts by activities (i.e., hierarchical plans associated with goals) and employ the concept of an intentional agent to reason about both normal and exceptional scenarios. We exemplify the application of this methodology by answering questions about a number of restaurant stories. This paper is under consideration for acceptance in TPLP.

There has recently been an increasing interest in declarative data analysis, where analytic tasks are specified using a logical language, and their implementation and optimisation are delegated to a general-purpose query engine. Existing declarative languages for data analysis can be formalised as variants of logic programming equipped with arithmetic function symbols and/or aggregation, and are typically undecidable. In prior work, the language of $\mathit{limit\ programs}$ was proposed, which is sufficiently powerful to capture many analysis tasks and has decidable entailment problem. Rules in this language, however, do not allow for negation. In this paper, we study an extension of limit programs with stratified negation-as-failure. We show that the additional expressive power makes reasoning computationally more demanding, and provide tight data complexity bounds. We also identify a fragment with tractable data complexity and sufficient expressivity to capture many relevant tasks.

This article describes a Turing machine which can solve for $\beta^{'}$ which is RE-complete. RE-complete problems are proven to be undecidable by Turing's accepted proof on the Entscheidungsproblem. Thus, constructing a machine which decides over $\beta^{'}$ implies inconsistency in ZFC. We then discover that unrestricted use of the axiom of substitution can lead to hidden assumptions in a certain class of proofs by contradiction. These hidden assumptions create an implied axiom of incompleteness for ZFC. Later, we offer a restriction on the axiom of substitution by introducing a new axiom which prevents impredicative tautologies from producing theorems. Our discovery in regards to these foundational arguments, disproves the SPACE hierarchy theorem which allows us to solve the P vs NP problem using a TIME-SPACE equivalence oracle.

Spatial information is often expressed using qualitative terms such as natural language expressions instead of coordinates; reasoning over such terms has several practical applications, such as bus routes planning. Representing and reasoning on trajectories is a specific case of qualitative spatial reasoning that focuses on moving objects and their paths. In this work, we propose two versions of a trajectory calculus based on the allowed properties over trajectories, where trajectories are defined as a sequence of non-overlapping regions of a partitioned map. More specifically, if a given trajectory is allowed to start and finish at the same region, 6 base relations are defined (TC-6). If a given trajectory should have different start and finish regions but cycles are allowed within, 10 base relations are defined (TC-10). Both versions of the calculus are implemented as ASP programs; we propose several different encodings, including a generalised program capable of encoding any qualitative calculus in ASP. All proposed encodings are experimentally evaluated using a real-world dataset. Experiment results show that the best performing implementation can scale up to an input of 250 trajectories for TC-6 and 150 trajectories for TC-10 for the problem of discovering a consistent configuration, a significant improvement compared to previous ASP implementations for similar qualitative spatial and temporal calculi. This manuscript is under consideration for acceptance in TPLP.

A semantical embedding of input/output logic in classical higher-order logic is presented. This embedding enables the mechanisation and automation of reasoning tasks in input/output logic with off-the-shelf higher-order theorem provers and proof assistants. The key idea for the solution presented here results from the analysis of an inaccurate previous embedding attempt, which we will discuss as well.

The automated theorem prover Leo-III for classical higher-order logic with Henkin semantics and choice is presented. Leo-III is based on extensional higher-order paramodulation and accepts every common TPTP dialect (FOF, TFF, THF), including their recent extensions to rank-1 polymorphism (TF1, TH1). In addition, the prover natively supports almost every normal higher-order modal logic. Leo-III cooperates with first-order reasoning tools using translations to many-sorted first-order logic and produces verifiable proof certificates. The prover is evaluated on heterogeneous benchmark sets.

This paper builds on the recent ASPIC+ formalism, to develop a general framework for argumentation with preferences. We motivate a revised definition of conflict free sets of arguments, adapt ASPIC+ to accommodate a broader range of instantiating logics, and show that under some assumptions, the resulting framework satisfies key properties and rationality postulates. We then show that the generalised framework accommodates Tarskian logic instantiations extended with preferences, and then study instantiations of the framework by classical logic approaches to argumentation. We conclude by arguing that ASPIC+'s modelling of defeasible inference rules further testifies to the generality of the framework, and then examine and counter recent critiques of Dung's framework and its extensions to accommodate preferences.

The spread of autonomous systems into safety-critical areas has increased the demand for their formal verification, not only due to stronger certification requirements but also to public uncertainty over these new technologies. However, the complex nature of such systems, for example, the intricate combination of discrete and continuous aspects, ensures that whole system verification is often infeasible. This motivates the need for novel analysis approaches that modularise the problem, allowing us to restrict our analysis to one particular aspect of the system while abstracting away from others. For instance, while verifying the real-time properties of an autonomous system we might hide the details of the internal decision-making components. In this paper we describe verification of a range of properties across distinct dimesnions on a practical hybrid agent architecture. This allows us to verify the autonomous decision-making, real-time aspects, and spatial aspects of an autonomous vehicle platooning system. This modular approach also illustrates how both algorithmic and deductive verification techniques can be applied for the analysis of different system subcomponents.

Recent work in natural language processing has looked at learning text to code translation models using parallel pairs of text and code samples from example source code libraries (for a review, see Neubig (2016)). In particular, Richardson and Kuhn (2017a,b); Richardson et al. (2018) look at learning to translate short text descriptions to function signature representations as a first step towards modeling the semantics of function documentation. Examples pairs of docstring and function signature representations are shown in Figure 1; using such pairs, the goal is to learn a general model that can robustly translate a given description of a function to a formal representation of that function. Initially, these datasets were proposed as a synthetic resource for studying semantic parser induction (Mooney, 2007), or for building models that learn to translate text to formal meaning representations from parallel data (see Richardson et al. (2017) for a proposal on using these datasets for the inverse problem of data-to-text generation). To date, we have built around 45 API datasets across 11 popular programming languages (e.g., Python, Java, C, Scheme, Haskell, PHP) and 7 natural languages (see Richardson (2017)), each using an ad hoc rendering of the target function signature representations. In this brief note, we define a unified syntax for expressing these representations, as well as a systematic mapping into first-order logic and a small subject domain model. In doing this, we aim to answer the following question: what do these function signatures that are being learned actually mean, and how can they be used for solving more complex natural language understanding problems (for a similar idea, see Bos (2016))? By recasting the learned representations in terms of classical logic, the hope is that our datasets will in particular be made more accessible to studies on natural language based program synthesis (Raza et al., 2015) and natural language programming more generally. In what follows, we first define a general syntax for these representations, then discuss the mapping into logic and the various applications that motivate our particular approach and subject domain model.