ABSTRACT. Answer Set Programming (ASP) is a logic programming based paradigm for knowledge representation and reasoning and has been successfully used for automating commonsense reasoning. A unique feature of ASP is that it adopts inductive semantics for programs that are negation free. This means that given a program containing a positive cycle, only those models are admissible that assign the value false to all the propositions appearing in the positive cycle. If we adopt coinductive semantics, models that assign true to all the proposition can also be admitted. In this talk we will discuss coinductive ASP, its semantics, and implementation in the s(CASP) goal-directed predicate answer set programming systems. We will also discuss applications of coinductive ASP.

ABSTRACT. We consider the class of finite spiked Boolean algebras introduced by Inamdar and show that the modal and intermediate logics associated to it are not finitely axiomatisable.

ABSTRACT. In logic, quantifiers typically have an implicit linear order of dependencies. Henkin introduced a more general framework for quantifier prefixes, allowing for partial orderings among quantifiers. These quantifiers, now known as Henkin quantifiers, have been extensively studied in logic and have found significant applications in linguistics, arithmetic, and descriptive complexity.

Surprisingly, bounded versions of Henkin quantifiers, which restrict the range of these quantifiers, have not been explored. This paper defines bounded Henkin quantifiers and examines their properties from a complexity-theoretic perspective. In particular, we show that the set of predicates definable by quantifier-free formulas prefixed by a bounded Henkin quantifier is exactly NEXP. The proof goes via machine models defined using bounded Henkin quantifiers. Finally, we show that formulas with Henkin quantifiers define a complexity class contained in Delta_2 in the exponential hierarchy and define a natural complete problem for this class.

ABSTRACT. The use of monoids in the study of word languages recognized by finite-state automata has been quite fruitful. A key result is that the transition monoid of the minimal finite-state automaton recognizing a language is exactly the same as the syntactic monoid of the language. This enables the study of languages using algebraic tools, in particular the structure theory of finite monoids. We thus get the celebrated theorem by Schützenberger that shows the equivalence of star-free languages and languages recognized by aperiodic monoids. There are also similar algebraic characterizations of locally and piecewise testable languages.

In addition to word languages, notions of recognizability have been defined for languages of trees, infinite words, timed words, and data languages but using morphisms into structures other than finite monoids. However, in this work, we look at the same idea of “recognizability by finite monoids” for other monoids. In particular, we see recognizable subsets of various additive and multiplicative monoids over integers, rationals, and reals. We see that while these recognizable sets satisfy properties such as closure under Boolean operations and inverse morphisms, they do not enjoy many of the nice properties that recognizable word languages do.

ABSTRACT. This talk presents an analysis of statements of reasons to / for / in favour of, as they appear, for example, in “The lineup of invited speakers is a reason to submit to ICLA / for submitting to ICLA / in favour of submitting to ICLA.”

We propose that reasons for are a species of reasons why. An example of a reason why statements is, “The lineup of speakers is a reason why I will submit to ICLA.” We assume that each proposition has a value (also known as a desirability or favourability) for the relevant agent of the proposition being true. We analyse reasons for in terms of reasons why and value, proposing that a reason for P is a reason why P has at least the value that it has.

To illustrate, suppose that submitting to ICLA has a value of 5 for the relevant agent. On this proposal, then, the lineup of speakers is a reason to submit to ICLA just in case the line up of speakers is a reason why submitting to ICLA has a value of at least 5. To analyse reasons why in turn, we adopt a recent analysis due to McHugh (2024).

ABSTRACT. There have been various attempts at training LLMs to perform deductive reasoning tasks. Some among these show that LLMs behave like humans by displaying content effect and imperfect abstract reasoning. Others, using chain-of-thought prompting, suggest that LLMs may emulate human-like thought processes without necessarily possessing reasoning competence. Still others conclude that language models do not yet demonstrate reliable deductive competence, since their performance is shown to decrease upon introduction of perturbations, such as synonym substitution.

In this study, we look at three distinct attempts at training LLMs on deductive competence tasks, each employing different criteria such as content-based reasoning (Dasgupta et al., 2023), chain-of-thought prompting (Wei et. al., 2023), and perturbations (Yuan et al., 2023). We then aim to introduce a framework to verify the claims regarding reasoning competence of each of the above studies. Based on the notion that deductive competence involves the following of rules of logic, we propose the use of the Wittgensteinian distinction between rule-following (Proudfoot 2004) and quasi-rule following as a method to distinguish genuine deductive competence from quasi-competence. The criteria distinguishing between rule-following and quasi-rule following shall be adapted to analyze whether these LLMs can be said to reason genuinely or are merely imitating reasoning-like behavior.

ABSTRACT. Reasoning about knowledge of multiple agents has been a steady line of research that has been motivated by applications in distributed systems, artificial intelligence, etc. This resulted in the emergence of various logical frameworks, most of them involving modal logics, in particular epistemic logics, that involve modeling using Kripke models. One of those applications involve automated planning. The most important problem in planning is whether there is a plan to achieve a goal from an initial state. Besides classical planning, epistemic planning has emerged as a line of study where the goal may involve what an agent knows about other agents' knowledge in various scenarios. Moreover, with the introduction of Dynamic Epistemic Logic ($\DEL$), this has gained much significance. $\DEL$ is an extension of Epistemic logic, where in addition to reasoning about knowledge, it introduces actions that result in change of such knowledge. Naturally, the model-checking and satisfiability problems of $\DEL$ caught much attention in solving plan-existence problem for Epistemic planning. Even though the model-checking problem of $\DEL$ is proven to be $\PSPACE$-Complete, the epistemic plan-existence problem is undecidable. This occurs due to the fact that the plan-existence problem can decide whether there is a finite iteration of some actions which causes a knowledge change. Hence, studying variants of $\DEL$ can help in bringing decidable fragments of Epistemic planning. One such logical framework is the Public Observation Logic ($\POL$). This framework enables reasoning about how knowledge changes with respect to public observations. Agents here cannot distinguish among possibilities, each of which has facts, like $\DEL$, as well as expected observations, which get updated. These observations are interpreted using regular expressions, hence it enables to interpret whether there exists some finite iteration of some observations using Kleene Star. We have studied the alogrithmic aspects of this formal framework. To be specific, the model-checking and satisfiability problem of $\POL$ has been explored. We prove that the model-checking problem is $\PSPACE$-Complete~\cite{polmcijcai}, whereas the satisfiability problem without allowing Kleene Star is $\NEXPTIME$-Complete~\cite{polsfsatkr}. Decidable fragment of plan-existence problem of Epistemic planning is a direct application of these results. One of the properties that make it decidable is that each observation is public, whereas in $\DEL$ private actions can also be considered.