Large Language Models (LLMs) excel at understanding natural language but struggle with explicit commonsense reasoning. A recent trend of research suggests that the combination of LLM with robust symbolic reasoning systems can overcome this problem on story-based question answering tasks. In this setting, existing approaches typically depend on human expertise to manually craft the symbolic component. We argue, however, that this component can also be automatically learned from examples. In this work, we introduce LLM2LAS, a hybrid system that effectively combines the natural language understanding capabilities of LLMs, the rule induction power of the Learning from Answer Sets (LAS) system ILASP, and the formal reasoning strengths of Answer Set Programming (ASP). LLMs are used to extract semantic structures from text, which ILASP then transforms into interpretable logic rules. These rules allow an ASP solver to perform precise and consistent reasoning, enabling correct answers to previously unseen questions. Empirical results outline the strengths and weaknesses of our automatic approach for learning and reasoning in a story-based question answering benchmark.

We present the solver asp-fzn for Constraint Answer Set Programming (CASP), which extends ASP with linear constraints. Our approach is based on translating CASP programs into the solver-independent FlatZinc language that supports several Constraint Programming and Integer Programming backend solvers. Our solver supports a rich language of linear constraints, including some common global constraints. As for evaluation, we show that asp-fzn is competitive with state-of-the-art ASP solvers on benchmarks taken from past ASP competitions. Furthermore, we evaluate it on several CASP problems from the literature and compare its performance with clingcon, which is a prominent CASP solver that supports most of the asp-fzn language. The performance of asp-fzn is very promising as it is already competitive on plain ASP and even outperforms clingcon on some CASP benchmarks.

Recently an extension to higher-order logic -- called DHOL -- was introduced, enriching the language with dependent types, and creating a powerful extensional type theory. In this paper we propose two ways how choice can be added to DHOL. We extend the DHOL term structure by Hilbert's indefinite choice operator $\epsilon$, define a translation of the choice terms to HOL choice that extends the existing translation from DHOL to HOL and show that the extension of the translation is complete and give an argument for soundness. We finally evaluate the extended translation on a set of dependent HOL problems that require choice.

In online combinatorial allocations/auctions, n bidders sequentially arrive, each with a combinatorial valuation (such as submodular/XOS) over subsets of m indivisible items. The aim is to immediately allocate a subset of the remaining items to maximize the total welfare, defined as the sum of bidder valuations. A long line of work has studied this problem when the bidder valuations come from known independent distributions. In particular, for submodular/XOS valuations, we know 2-competitive algorithms/mechanisms that set a fixed price for each item and the arriving bidders take their favorite subset of the remaining items given these prices. However, these algorithms traditionally presume the availability of the underlying distributions as part of the input to the algorithm. Contrary to this assumption, practical scenarios often require the learning of distributions, a task complicated by limited sample availability. This paper investigates the feasibility of achieving O(1)-competitive algorithms under the realistic constraint of having access to only a limited number of samples from the underlying bidder distributions. Our first main contribution shows that a mere single sample from each bidder distribution is sufficient to yield an O(1)-competitive algorithm for submodular/XOS valuations. This result leverages a novel extension of the secretary-style analysis, employing the sample to have the algorithm compete against itself. Although online, this first approach does not provide an online truthful mechanism. Our second main contribution shows that a polynomial number of samples suffices to yield a $(2+\epsilon)$-competitive online truthful mechanism for submodular/XOS valuations and any constant $\epsilon>0$. This result is based on a generalization of the median-based algorithm for the single-item prophet inequality problem to combinatorial settings with multiple items.

Answer Set Programming with Quantifiers (ASP(Q)) has been introduced to provide a natural extension of ASP modeling to problems in the polynomial hierarchy (PH). However, ASP(Q) lacks a method for encoding in an elegant and compact way problems requiring a polynomial number of calls to an oracle in $\Sigma_n^p$ (that is, problems in $\Delta_{n+1}^p$). Such problems include, in particular, optimization problems. In this paper we propose an extension of ASP(Q), in which component programs may contain weak constraints. Weak constraints can be used both for expressing local optimization within quantified component programs and for modeling global optimization criteria. We showcase the modeling capabilities of the new formalism through various application scenarios. Further, we study its computational properties obtaining complexity results and unveiling non-obvious characteristics of ASP(Q) programs with weak constraints.

The representation of a dynamic problem in ASP usually boils down to using copies of variables and constraints, one for each time stamp, no matter whether it is directly encoded or via an action or temporal language. The multiplication of variables and constraints is commonly done during grounding and the solver is completely ignorant about the temporal relationship among the different instances. On the other hand, a key factor in the performance of today's ASP solvers is conflict-driven constraint learning. Our question is now whether a constraint learned for particular time steps can be generalized and reused at other time stamps, and ultimately whether this enhances the overall solver performance on temporal problems. Knowing full well the domain of time, we study conditions under which learned dynamic constraints can be generalized. We propose a simple translation of the original logic program such that, for the translated programs, the learned constraints can be generalized to other time points. Additionally, we identify a property of temporal problems that allows us to generalize all learned constraints to all time steps. It turns out that this property is satisfied by many planning problems. Finally, we empirically evaluate the impact of adding the generalized constraints to an ASP solver.

Graphical structures estimated by causal learning algorithms from time series data can provide highly misleading causal information if the causal timescale of the generating process fails to match the measurement timescale of the data. Although this problem has been recently recognized, practitioners have limited resources to respond to it, and so must continue using models that they know are likely misleading. Existing methods either (a) require that the difference between causal and measurement timescales is known; or (b) can handle only very small number of random variables when the timescale difference is unknown; or (c) apply to only pairs of variables, though with fewer assumptions about prior knowledge; or (d) return impractically too many solutions. This paper addresses all four challenges. We combine constraint programming with both theoretical insights into the problem structure and prior information about admissible causal interactions. The resulting system provides a practical approach that scales to significantly larger sets (>100) of random variables, does not require precise knowledge of the timescale difference, supports edge misidentification and parametric connection strengths, and can provide the optimum choice among many possible solutions. The cumulative impact of these improvements is gain of multiple orders of magnitude in speed and informativeness.

This paper introduces a class of objects called decision rules that map infinite sequences of alternatives to a decision space. These objects can be used to model situations where a decision maker encounters alternatives in a sequence such as receiving recommendations. Within the class of decision rules, we study natural subclasses: stopping and uniform stopping rules. Our main result establishes the equivalence of these two subclasses of decision rules. Next, we introduce the notion of computability of decision rules using Turing machines and show that computable rules can be implemented using a simpler computational device: a finite automaton. We further show that computability of choice rules -- an important subclass of decision rules -- is implied by their continuity with respect to a natural topology. Finally, we introduce some natural heuristics in this framework and provide their behavioral characterization.

We take up an idea from the folklore of Answer Set Programming, namely that choices, integrity constraints along with a restricted rule format is sufficient for Answer Set Programming. We elaborate upon the foundations of this idea in the context of the logic of Here-and-There and show how it can be derived from the logical principle of extension by definition. We then provide an austere form of logic programs that may serve as a normalform for logic programs similar to conjunctive normalform in classical logic. Finally, we take the key ideas and propose a modeling methodology for ASP beginners and illustrate how it can be used.

Answer Set Programming (ASP) [4, 5] is a popular paradigm for decision making and problem solving in Knowledge Representation and Reasoning. It has been successfully applied in a variety of applications such as robotics, planning, diagnosis, etc. ASP is an attractive programming paradigm as it is a declarative language, where programmers focus on the representation of a specific problem as a set of rules in a logical format, and then leave computational solutions of that problem to an answer set solver. However, this mechanism typically gives little insight into why something is a solution and why some proposed set of literals is not a solution. This type of reasoning falls within the scope of explainable Artificial Intelligence and is useful to enhance the understanding of the resulting solutions as well as for debugging programs. So far, only a limited number of approaches have been proposed [1, 6, 7].