Related papers: Satisfiability of Short Circuit Logic
The problem of estimating the proportion of satisfiable instances of a given CSP (constraint satisfaction problem) can be tackled through weighting. It consists in putting onto each solution a non-negative real value based on its…
This is the author's Ph.D. Thesis. It contains results from four years of research into realizability and categorical logic. The main subjects are the axiomatisation of realizable propositions, and a characterization of realizability…
We investigate the possibility of a semantic account of the execution time (i.e. the number of beta-steps leading to the normal form, if any) for the shuffling calculus, an extension of Plotkin's call-by-value lambda-calculus. For this…
We describe a graph-theoretic syntax for self-referential formulas as well as a four-valued logic to include contradictory and independent formulas. We then explore the degree to which generalized truth tables can be realized in our theory,…
We make explicit the correspondence between syntax and syntactic categories for coherent first-order logic, providing a categorical characterization of bi-interpretability. This is done by creating a biequivalence between a bicategory of…
The standard reasoning problem, concept satisfiability, in the basic description logic ALC is PSPACE-complete, and it is EXPTIME-complete in the presence of unrestricted axioms. Several fragments of ALC, notably logics in the FL, EL, and…
Temporal logics for the specification of information-flow properties are able to express relations between multiple executions of a system. The two most important such logics are HyperLTL and HyperCTL*, which generalise LTL and CTL* by…
Large Language Models (LLMs) employing Chain-of-Thought (CoT) prompting have broadened the scope for improving multi-step reasoning capabilities. We generally divide multi-step reasoning into two phases: path generation to generate the…
Convincing someone of the truth value of a premise requires understanding and articulating the core logical structure of the argument which proves or disproves the premise. Understanding the logical structure of an argument refers to…
Satisfiability solving is a common technique for formal verification forming the basis of many proof and model checking systems. Failure to show a proof obligation will produce a counterexample or failure trace with typically many thousands…
We study formal languages which are capable of fully expressing quantitative probabilistic reasoning and do-calculus reasoning for causal effects, from a computational complexity perspective. We focus on satisfiability problems whose…
We present here a SAT-based framework for LTLf (Linear Temporal Logic on Finite Traces) satisfiability checking. We use propositional SAT-solving techniques to construct a transition system for the input LTLf formula; satisfiability…
Over the past two decades several fragments of first-order logic have been identified and shown to have good computational and algorithmic properties, to a great extent as a result of appropriately describing the image of the standard…
Prompt Engineering has garnered significant attention for enhancing the performance of large language models across a multitude of tasks. Techniques such as the Chain-of-Thought not only bolster task performance but also delineate a clear…
The logic of definitions is a family of logics for encoding and reasoning about judgments, which are atomic predicates specified by inference rules. A definition associates an atomic predicate with a logical formula, which may itself depend…
Linear logic provides a framework to control the complexity of higher-order functional programs. We present an extension of this framework to programs with multithreading and side effects focusing on the case of elementary time. Our main…
We introduce two variants of computation tree logic CTL based on team semantics: an asynchronous one and a synchronous one. For both variants we investigate the computational complexity of the satisfiability as well as the model checking…
Matching logic is a logical framework for specifying and reasoning about programs using pattern matching semantics. A pattern is made up of a number of structural components and constraints. Structural components are syntactically matched,…
Hybrid branching-time logics are introduced as extensions of CTL-like logics with state variables and the downarrow-binder. Following recent work in the linear framework, only logics with a single variable are considered. The expressive…
The finite satisfiability problem for the two-variable fragment of first-order logic interpreted over trees was recently shown to be ExpSpace-complete. We consider two extensions of this logic. We show that adding either additional binary…