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## Publications

Publications (20)

Proofs from assumptions are amongst the most fundamental reasoning techniques. Yet the precise nature of assumptions is still an open topic. One of the most prominent conceptions is the placeholder view of assumptions generally associated with natural deduction for intuitionistic propositional logic. It views assumptions essentially as holes in pro...

In this paper we examine two approaches to the formal treatment of the notion of problem in the paradigm of algorithmic semantics. Namely, we will explore an approach based on Martin-Löf’s Constructive Type Theory (CTT), which can be seen as a direct continuation of Kolmogorov’s original calculus of problems, and an approach utilizing Tichý’s Trans...

In his recent book The Impossible: An Essay on Hyperintensionality (2014) Jago states that proof-theoretic semantics (PTS) does not easily deliver hyperintensional contents. I argue against this claim and show that, on the contrary, hyperintensionality is one of the basic features of PTS approaches.

The main objective of this paper is to sketch unifying conceptual and formal framework for inference that is able to explain various proof techniques without implicitly changing the underlying notion of inference rules. We base this framework upon the so-called two-dimensional, i.e., deduction to deduction, account of inference introduced by Tichý...

In Transparent Intensional Logic we can recognize two distinct notions of computation that loosely correspond to term rewriting and term interpretation as known from lambda calculus. Our goal will be to further explore these two notions and examine some of their properties.

Proofs from assumptions are amongst the most fundamental reasoning techniques. Yet the precise nature of assumptions is still an open topic. One of the most prominent conceptions is the placeholder view of assumptions generally associated with natural deduction for intuitionistic propositional logic. It views assumptions essentially as holes in pro...

In this paper, we will be interested in the notion of a computable proposition. It allows for feasible computational semantics of empirical sentences, despite the fact that it is in general impossible to get to the truth value of a sentence through a series of effective computational steps. Specifically, we will investigate two approaches to the no...

Kosta Došen argued in his papers Inferential Semantics (in Wansing, H. (ed.) Dag Prawitz on Proofs and Meaning, pp. 147–162. Springer, Berlin 2015) and On the Paths of Categories (in Piecha, T., Schroeder-Heister, P. (eds.) Advances in Proof-Theoretic Semantics, pp. 65–77. Springer, Cham 2016) that the propositions-as-types paradigm is less suited...

We approach the topic of solution equivalence of propositional problems from the perspective of non-constructive procedural theory of problems based on Transparent Intensional Logic (TIL). The answer we put forward is that two solutions are equivalent if and only if they have equivalent solution concepts. Solution concepts can be understood as a ge...

The problem of hyperintensional contexts, and the problem of logical omniscience, shows the severe limitation of possible-worlds semantics which is employed also in standard epistemic logic. As a solution, we deploy here hyperintensional semantics according to which the meaning of an expression is an abstract structured algorithm, namely Tichý’s co...

Recenze knihy: Pavel Materna. Hovory o pojmu. Praha: Academia, 2016, 158 stran.

The aim of this paper is to draft a conceptual framework for explicating desires, and to outline basic mechanisms for reasoning model based upon these desires. The explication will be framed in the system of Transparent Intensional Logic (TIL).

In this paper we revisit Pavel Tichý's novel distinction between one-dimensional and two-dimensional conception of inference, which he presented in his book Foundations of Frege's Logic (1988), and later in On Inference (1999), which was prepared from his manuscript by his co-author Jindra Tichý. We shall focus our inquiry not only on the motivatio...

Nemonotonni logika vznikla za ucelem systematicky zachytit tzv. zrusitelne uvažovani, tj. typ každodenniho uvažovani, ktere vede jen k provizorně platným argumentům, jenž mohou být nasledně staženy s přichodem nových informaci. Tim se ovsem nemonotonni logika dostava do ostreho kontrastu s klasickou logikou, ktera je monotonni, tj. žadne dodatecne...