Expressive Logics for Coinductive Predicates

The classical Hennessy-Milner theorem says that two states of an image-finite transition system are bisimilar if and only if they satisfy the same formulas in a certain modal logic. In this paper we study this type of result in a general context, moving from transition systems to coalgebras and from bisimilarity to coinductive predicates. We formulate when a logic fully characterises a coinductive predicate on coalgebras, by providing suitable notions of adequacy and expressivity, and give sufficient conditions on the semantics. The approach is illustrated with logics characterising similarity, divergence and a behavioural metric on automata

Coalgebra Learning via Duality

Automata learning is a popular technique for inferring minimal automata through membership and equivalence queries. In this paper, we generalise learning to the theory of coalgebras. The approach relies on the use of logical formulas as tests, based on a dual adjunction between states and logical theories. This allows us to learn, e.g., labelled transition systems, using Hennessy-Milner logic. Our main contribution is an abstract learning algorithm, together with a proof of correctness and termination

Equality-friendly well-founded semantics and applications to description logics

We tackle the problem of defining a well-founded semantics (WFS) for Datalog rules with existentially quantified variables in their heads and nega- tions in their bodies. In particular, we provide a WFS for the recent Datalog± family of ontology languages, which covers several important description logics (DLs). To do so, we generalize Datalog± by non-stratified nonmonotonic nega- tion in rule bodies, and we define a WFS for this generalization via guarded fixed point logic. We refer to this approach as equality-friendly WFS, since it has the advantage that it does not make the unique name assumption (UNA); this brings it close to OWL and its profiles as well as typical DLs, which also do not make the UNA. We prove that for guarded Datalog± with negation under the equality- friendly WFS, conjunctive query answering is decidable, and we provide precise complexity results for this problem. From these results, we obtain precise defi- nitions of the standard WFS extensions of EL and of members of the DL-Lite family, as well as corresponding complexity results for query answering

Well-Founded Semantics for Extended Datalog and Ontological Reasoning

The Datalog± family of expressive extensions of Datalog has recently been introduced as a new paradigm for query answering over ontologies, which captures and extends several common description logics. It extends plain Datalog by features such as existentially quantified rule heads and, at the same time, restricts the rule syntax so as to achieve decidability and tractability. In this paper, we continue the research on Datalog±. More precisely, we generalize the well-founded semantics (WFS), as the standard semantics for nonmonotonic normal programs in the database context, to Datalog± programs with negation under the unique name assumption (UNA). We prove that for guarded Datalog± with negation under the standard WFS, answering normal Boolean conjunctive queries is decidable, and we provide precise complexity results for this problem, namely, in particular, completeness for PTIME (resp., 2-EXPTIME) in the data (resp., combined) complexity

Measure-Theoretic Semantics for Quantitative Parity Automata

Quantitative parity automata (QPAs) generalise non-deterministic parity automata (NPAs) by adding weights from a certain semiring to transitions. QPAs run on infinite word/tree-like structures, modelled as coalgebras of a polynomial functor F. They can also arise as certain products between a quantitative model (with branching modelled via the same semiring of quantities, and linear behaviour described by the functor F) and an NPA (modelling a qualitative property of F-coalgebras). We build on recent work on semiring-valued measures to define a way to measure the set of paths through a quantitative branching model which satisfy a qualitative property (captured by an unambiguous NPA running on F-coalgebras). Our main result shows that the notion of extent of a QPA (which generalises non-emptiness of an NPA, and is defined as the solution of a nested system of equations) provides an equivalent characterisation of the measure of the accepting paths through the QPA. This result makes recently-developed methods for computing nested fixpoints available for model checking qualitative, linear-time properties against quantitative branching models

DNA methylation and transcriptional control in memory formation, persistence and suppression

Memory formation is a complex process regulated by various molecular mechanisms, including unique transcriptional signatures and epigenetic factors. In addition, the brain is equipped with mechanisms that not only promote, but actively constrict memory formation. While the role of epigenetic modifications, such as DNA methylation, in cognition has been established, there are still significant gaps in our understanding of the specific functions of individual DNA methyltransferases (Dnmts) and how their downstream effectors orchestrate memory. Moreover, the molecular mechanisms underlying memory persistence and memory suppression remain largely unexplored. I investigated the role of specific Dnmts in long-term memory formation, highlighting their unique functions and downstream effects. Additionally, I explored how DNA methylation contributes to the transfer of information from the hippocampus to the cortex for long-term storage and the stabilisation of cortical engrams to drive memory persistence. First, I examined the involvement of Dnmt3a1, the predominant Dnmt3a isoform in the adult brain, in hippocampus-dependent long-term memory formation. I identified an activity-regulated Dnmt3a1-dependent gene expression program and found a downstream effector gene (Neuropilin-1) with a previously undescribed function in memory formation. Intriguingly, I found that despite a common requirement for memory formation, Dnmt3a1 and Dnmt3a2 regulate this process via distinct mechanisms - Nrp1 overexpression rescued Dnmt3a1, but not Dnmt3a2, knockdown-driven impairments in memory formation. Next, I investigated the molecular mechanisms underlying memory persistence and systems consolidation, the gradual transfer of information from the hippocampus to the cortex. By modulating DNA methylation processes in the dorsal hippocampus, a short-lasting memory could be converted into a long-lasting one. The applied manipulation resulted in improved reactivation of cortical engrams and increased fear generalisation, mimicking the characteristics of remote memory. These findings provide compelling evidence for the facilitatory role of DNA methylation in memory information transfer to the cortex for long-term storage. Furthermore, I examined the temporal expression patterns of immediate early genes (IEGs), specifically neuronal PAS domain protein 4 (Npas4), and its potential role in memory suppression. My investigation revealed that highly salient stimuli induced a biphasic expression of Npas4 in the hippocampus, with the later phase dependent on NMDA receptor activity. Notably, this later phase of Npas4 expression restricted memory consolidation, suggesting a role in balancing the formation of highly salient memories and preventing the development of maladaptive behaviours. These findings highlighted the intricate regulatory network by which experience salience modulates IEG expression and thereby fine-tunes memory consolidation. Overall, this study uncovered the unique functions of distinct Dnmts in memory formation and persistence and shed light on the associated mechanisms that are responsible to facilitate the transfer of information required for long-term storage. This comprehensive understanding of the molecular processes underlying memory formation contributes to our broader knowledge of memory consolidation and may have implications for therapeutic interventions targeting memory-related disorders

Coalgebraic Automata Theory: Basic Results

We generalize some of the central results in automata theory to the abstraction level of coalgebras and thus lay out the foundations of a universal theory of automata operating on infinite objects. Let F be any set functor that preserves weak pullbacks. We show that the class of recognizable languages of F-coalgebras is closed under taking unions, intersections, and projections. We also prove that if a nondeterministic F-automaton accepts some coalgebra it accepts a finite one of the size of the automaton. Our main technical result concerns an explicit construction which transforms a given alternating F-automaton into an equivalent nondeterministic one, whose size is exponentially bound by the size of the original automaton.Comment: 43 page

Angluin learning via logic

In this paper we will provide a fresh take on Dana Angluin's algorithm for learning using ideas from coalgebraic modal logic. Our work opens up possibilities for applications of tools & techniques from modal logic to automata learning and vice versa. As main technical result we obtain a generalisation of Angluin's original algorithm from DFAs to coalgebras for an arbitrary finitary set functor T in the following sense: given a (possibly infinite) pointed T-coalgebra that we assume to be regular (i.e. having an equivalent finite representation) we can learn its finite representation by asking (i) "logical queries" (corresponding to membership queries) and (ii) making conjectures to which the teacher has to reply with a counterexample. This covers (a known variant) of the original L* algorithm and the learning of Mealy/Moore machines. Other examples are bisimulation quotients of (probabilistic) transition systems

No Champion for Children: Tennessee\u27s Rule 40A and the Appointment of Guardians ad Litem in Custody Proceedings

On February 17, 2009, the Tennessee Supreme Court adopted a provisional rule to be used in child custody cases in all courts in the State of Tennessee.\u27 The rule, Rule 40A, concerns the Appointment of Guardians Ad Litem in Custody Proceedings and dictates the appointment, role, powers, duties, rights, limitations, and costs of guardians ad litem in limited types of cases including but not limited to divorce, paternity, domestic violence, contested adoptions, and contested private guardianship cases. Rule 40A is provisional in that it was passed with the intention of it lasting only a limited time while the mechanics of the rule were evaluated and commented on by the general public and members of the bench and private bars