Browsing by Subject "Automated theorem proving"

Now showing 1 - 3 of 3

Open Access
A backwards theorem prover with focusing, resource management and constraints for robotic planning within intuitionistic linear logic
(2010) Kortik, Sıtar
The main scope of this thesis is implementing a backwards theorem prover with focusing, resource management and constraints within the intuitionistic first-order linear logic for robotic planning problems. To this end, backwards formulations provide a simpler context for experimentation. However, existing backward theorem provers are either implemented without regard to the efficiency of the proofsearch, or when they do, restrict the language to smaller fragments such as Linear Hereditary Harrop Formulas (LHHF). The former approach is unsuitable since it significantly impairs the scalability of the resulting system. The latter family of theorem provers address the scalability issue but impact the expressivity of the resulting language and may not be able to deal with certain non-deterministic planning elements. The proof theory we describe in this thesis enables us to effectively experiment with the use of linearity and continuous constraints to encode dynamic state elements characteristic of robotic planning problems. To this end, we describe a prototype implementation of our system in SWI-Prolog, and also incorporate continuous constraints into the prototype implementation of the system. We support the expressivity and efficiency of our system with some examples.
Open Access
Experiments in integrating constraints with logical reasoning for robotic planning within the twelf logical framework and the prolog language
(2008) Duatepe, Mert
The underlying domain of various application areas, especially real-time systems and robotic applications, generally includes a combination of both discrete and continuous properties. In robotic applications, a large amount of different approaches are introduced to solve either a discrete planning or control theoretic problem. Only a few methods exist to solve the combination of them. Moreover, these methods fail to ensure a uniform treatment of both aspects of the domain. Therefore, there is need for a uniform framework to represent and solve such problems. A new formalism, the Constrained Intuitionistic Linear Logic (CILL), combines continuous constraint solvers with linear logic. Linear logic has a great property to handle hypotheses as resources, easily solving state transition problems. On the other hand, constraint solvers deal well with continuous problems defined as constraints. Both properties of CILL gives us powerful ways to express and reason about the robotics domain. In this thesis, we focus on the implementation of CILL in both the Twelf Logical Framework and Prolog. The reader of this thesis can find answers of why classical aspects are not proper for the robotics domain, what advantages one can gain from intuitionism and linearity, how one can define a simple robotic domain in a logical formalism, how a proof in logical system corresponds to a plan in the robotic domain, what the advantages and disadvantages of logical frameworks and Prolog have and how the implementation of CILL can or cannot be done using both Twelf Logical Framework and Prolog.
Open Access
Robotic task planning using a backchaining theorem prover for multiplicative exponential first-order linear logic
(Springer, 2019) Kortik, Sitar; Saranlı, U.
In this paper, we propose an exponential multiplicative fragment of linear logic to encode and solve planning problems efficiently in STRIPS domain, that we call the Linear Planning Logic (LPL). Linear logic is a resource aware logic treating resources as single use assumptions, therefore enabling encoding and reasoning of domains with dynamic state. One of the most important examples of dynamic state domains is robotic task planning, since informational or physical states of a robot include non-monotonic characteristics. Our novel theorem prover is using the backchaining method which is suitable for logic languages like Lolli and Prolog. Additionally, we extend LPL to be able to encode non-atomic conclusions in program formulae. Following the introduction of the language, our theorem prover and its implementation, we present associated algorithmic properties through small but informative examples. Subsequently, we also present a navigation domain using the hexapod robot RHex to show LPL’s operation on a real robotic planning problem. Finally, we provide comparisons of LPL with two existing linear logic theorem provers, llprover and linTAP. We show that LPL outperforms these theorem provers for planning domains.