The Complexity and Expressive Power of Limit Datalog

Motivated by applications in declarative data analysis, in this article, we study Datalog Z —an extension of Datalog with stratified negation and arithmetic functions over integers. This language is known to be undecidable, so we present the fragment of limit Datalog Z programs, which is powerful enough to naturally capture many important data analysis tasks. In limit Datalog Z , all intensional predicates with a numeric argument are limit predicates that keep maximal or minimal bounds on numeric values. We show that reasoning in limit Datalog Z is decidable if a linearity condition restricting the use of multiplication is satisfied. In particular, limit-linear Datalog Z is complete for Δ 2 EXP and captures Δ 2 P over ordered datasets in the sense of descriptive complexity. We also provide a comprehensive study of several fragments of limit-linear Datalog Z . We show that semi-positive limit-linear programs (i.e., programs where negation is allowed only in front of extensional atoms) capture coNP over ordered datasets; furthermore, reasoning becomes coNEXP-complete in combined and coNP-complete in data complexity, where the lower bounds hold already for negation-free programs. In order to satisfy the requirements of data-intensive applications, we also propose an additional stability requirement, which causes the complexity of reasoning to drop to EXP in combined and to P in data complexity, thus obtaining the same bounds as for usual Datalog. Finally, we compare our formalisms with the languages underpinning existing Datalog-based approaches for data analysis and show that core fragments of these languages can be encoded as limit programs; this allows us to transfer decidability and complexity upper bounds from limit programs to other formalisms. Therefore, our article provides a unified logical framework for declarative data analysis which can be used as a basis for understanding the impact on expressive power and computational complexity of the key constructs available in existing languages.

Logics with Multiteam Semantics

Team semantics is the mathematical basis of modern logics of dependence and independence. In contrast to classical Tarski semantics, a formula is evaluated not for a single assignment of values to the free variables, but on a set of such assignments, called a team. Team semantics is appropriate for a purely logical understanding of dependency notions, where only the presence or absence of data matters, but being based on sets, it does not take into account multiple occurrences of data values. It is therefore insufficient in scenarios where such multiplicities matter, in particular for reasoning about probabilities and statistical independencies. Therefore, an extension from teams to multiteams (i.e. multisets of assignments) has been proposed by several authors. In this paper we aim at a systematic development of logics of dependence and independence based on multiteam semantics. We study atomic dependency properties of finite multiteams and discuss the appropriate meaning of logical operators to extend the atomic dependencies to full-fledged logics for reasoning about dependence properties in a multiteam setting. We explore properties and expressive power of a wide spectrum of different multiteam logics and compare them to second-order logic and to logics with team semantics. In many cases the results resemble what is known in team semantics, but there are also interesting differences. While in team semantics, the combination of inclusion and exclusion dependencies leads to a logic with the full power of both independence logic and existential second-order logic, independence properties of multiteams are not definable by any combination of properties that are downwards closed or union closed and thus are strictly more powerful than inclusion-exclusion logic. We also study the relationship of logics with multiteam semantics with existential second-order logic for a specific class of metafinite structures. It turns out that inclusion-exclusion logic can be characterised in a precise sense by the Presburger fragment of this logic, but for capturing independence, we need to go beyond it and add some form of multiplication. Finally, we also consider multiteams with weights in the reals and study the expressive power of formulae by means of topological properties.

Bounded Abstract Effects

Effect systems have been a subject of active research for nearly four decades, with the most notable practical example being checked exceptions in programming languages such as Java. While many exception systems support abstraction, aggregation, and hierarchy (e.g., via class declaration and subclassing mechanisms), it is rare to see such expressive power in more generic effect systems. We designed an effect system around the idea of protecting system resources and incorporated our effect system into the Wyvern programming language. Similar to type members, a Wyvern object can have effect members that can abstract lower-level effects, allow for aggregation, and have both lower and upper bounds, providing for a granular effect hierarchy. We argue that Wyvern’s effects capture the right balance of expressiveness and power from the programming language design perspective. We present a full formalization of our effect-system design, showing that it allows reasoning about authority and attenuation. Our approach is evaluated through a security-related case study.

Symmetric Circuits for Rank Logic

Fixed-point logic with rank (FPR) is an extension of fixed-point logic with counting (FPC) with operators for computing the rank of a matrix over a finit field. The expressive power of FPR properly extends that of FPC and is contained in P, but it is not known if that containment is proper. We give a circuit characterization for FPR in terms of families of symmetric circuits with rank gates, along the lines of that for FPC given by Anderson and Dawar in 2017. This requires the development of a broad framework of circuits in which the individual gates compute functions that are not symmetric (i.e., invariant under all permutations of their inputs). This framework also necessitates the development of novel techniques to prove the equivalence of circuits and logic. Both the framework and the techniques are of greater generality than the main result.

Reward Machines: Exploiting Reward Function Structure in Reinforcement Learning

Reinforcement learning (RL) methods usually treat reward functions as black boxes. As such, these methods must extensively interact with the environment in order to discover rewards and optimal policies. In most RL applications, however, users have to program the reward function and, hence, there is the opportunity to make the reward function visible – to show the reward function’s code to the RL agent so it can exploit the function’s internal structure to learn optimal policies in a more sample efficient manner. In this paper, we show how to accomplish this idea in two steps. First, we propose reward machines, a type of finite state machine that supports the specification of reward functions while exposing reward function structure. We then describe different methodologies to exploit this structure to support learning, including automated reward shaping, task decomposition, and counterfactual reasoning with off-policy learning. Experiments on tabular and continuous domains, across different tasks and RL agents, show the benefits of exploiting reward structure with respect to sample efficiency and the quality of resultant policies. Finally, by virtue of being a form of finite state machine, reward machines have the expressive power of a regular language and as such support loops, sequences and conditionals, as well as the expression of temporally extended properties typical of linear temporal logic and non-Markovian reward specification.

A Congruence-Based Perspective on Finite Tree Automata

We provide new insights on the determinization and minimization of tree automata using congruences on trees. From this perspective, we study a Brzozowski’s style minimization algorithm for tree automata. First, we prove correct this method relying on the following fact: when the automata-based and the language-based congruences coincide, determinizing the automaton yields the minimal one. Such automata-based congruences, in the case of word automata, are defined using pre and post operators. Now we extend these operators to tree automata, a task that is particularly challenging due to the reduced expressive power of deterministic top-down (or equivalently co-deterministic bottom-up) automata. We leverage further our framework to offer an extension of the original result by Brzozowski for word automata.

On the Expressive Power of Non-deterministic and Unambiguous Petri Nets over Infinite Words

We prove that ω-languages of (non-deterministic) Petri nets and ω-languages of (nondeterministic) Turing machines have the same topological complexity: the Borel and Wadge hierarchies of the class of ω-languages of (non-deterministic) Petri nets are equal to the Borel and Wadge hierarchies of the class of ω-languages of (non-deterministic) Turing machines. We also show that it is highly undecidable to determine the topological complexity of a Petri net ω-language. Moreover, we infer from the proofs of the above results that the equivalence and the inclusion problems for ω-languages of Petri nets are ∏21-complete, hence also highly undecidable. Additionally, we show that the situation is quite the opposite when considering unambiguous Petri nets, which have the semantic property that at most one accepting run exists on every input. We provide a procedure of determinising them into deterministic Muller counter machines with counter copying. As a consequence, we entail that the ω-languages recognisable by unambiguous Petri nets are △30 sets.

Expressive Power of Anti-Violence Legislation

abstract We know more about why laws on violence against women (vaw) were adopted than about how much and in what ways these laws affect society. The authors argue that even weakly enforced laws can contribute to positive social change. They theorize the expressive power of vaw legislation, and present evidence for a cautiously optimistic assessment of current trends on violence against women and the ways that vaw laws affect social norms. Focusing on a time of major legal change related to vaw in Mexico, this article explores trends in behavior and attitudes related to violence by analyzing four waves of the National Survey on the Dynamics of Household Relations (endireh), which include detailed interviews with thousands of Mexican women. The authors find that over this period, the share of women experiencing intimate-partner abuse declined, attitudes condoning violence shifted, reporting rates rose, and most women learned about legislation to protect their rights. These changes are consistent with the authors’ expectations about the expressive power of anti-violence legislation.

Translation Pragmatics of Phonic Expressive Means in English Poetic Texts

Phono-stylistics is a promising research area. Expressive power of a text depends on its phonetic imagery. The research objective was to identify the pragmatic features of phonic expressive means in translations of contemporary English poetry. The methods included a comparative analysis, phono-semantic and phono-stylistic interpretation of the original poems and their translations, and O. N. Tynyanov's law of versification. The method of sound counting developed by E. V. Elkina and L. S. Yudina was used to calculate the frequency of sounds in the context of phono-semantic analysis in the Russian translations. The method of sound counting designed by Tsoi Vi Chuen Thomas was used to calculate the frequency of sounds in the original English texts. The theoretical foundation of the research was formed by the works by M. A. Balash, G. V. Vekshin, Z. S. Dotmurzieva, V. N. Elkina, A. P. Zhuravlev, L. V. Laenko, F. Miko, L. P. Prokofyeva, E. A. Titov, etc. The study featured the phonics and pragmatics of S. Dugdale’s poem Zaitz and its three translations made by E. Tretyakova, A. Shchetinina, and M. Vinogradova, and C. E. Duffy’s Anne Hathaway translated by Yu. Fokina. The author compared the pragmatics of sound imagery in the English originals and their Russian translations. The research made it possible to define the role of sound imagery in the poetic discourse, as well as the relationship between the sound organization of poetic speech and the pragmatic value at the phonographic level. The results can be used in courses of translation, stylistics, and phonetics.

Pooling Modalities and Pointwise Intersection: Semantics, Expressivity, and Dynamics

We study classical modal logics with pooling modalities, i.e. unary modal operators that allow one to express properties of sets obtained by the pointwise intersection of neighbourhoods. We discuss salient properties of these modalities, situate the logics in the broader area of modal logics (with a particular focus on relational semantics), establish key properties concerning their expressive power, discuss dynamic extensions of these logics and provide reduction axioms for the latter.