• Phrasal Coordination Relatedness Logic
    Logic and Logical Philosophy 1-14. forthcoming.
    I presented a sub-classical relating logic based on a relating via an NL-inspired relating relation Rcss. The relation Rcss is motivated by the NL-phenomenon of phrasal (subsentential) coordination, exhibiting an important aspect of contents relating among the arguments of binary connectives. The resulting logic Lcss can be viewed as a relevance logic exhibiting a contents related relevance, stronger than the variable-sharing property of other relevance logics like R. Note that relating here is …Read more
  •  3
    Truth-Value Constants in Multi-Valued Logics
    with Michael Kaminski
    In Thomas Piecha & Kai F. Wehmeier (eds.), Peter Schroeder-Heister on Proof-Theoretic Semantics, Springer. pp. 391-397. 2024.
    In some presentations of classical and intuitionistic logics, the objectlanguage is assumed to contain (two) truth-value constants: ⊤ (verum) and ⊥ (falsum), that are, respectively, true and false under every bivalent valuation. We are interested to define and study analogical constants ‡, 1 ≤ i ≤ n, that in an arbitrary multi-valued logic over truth-values V = {v1,..., vn} have the truth-value vi under every (multi-valued) valuation. As is well known, the absence or presence of such constants h…Read more
  •  12
    A Dialectic Contra-Classical Logic
    Logica Universalis 17 (2): 221-229. 2023.
    The paper presents a contra-classical dialectic logic, inspired and motivated by Hegel s dialectics. Its axiom schemes are 0.1 Thus, in a sense, this dialectic logic is a kind of “mirror image“ of connexive logic. The informal interpretation of ‘ $$\rightarrow $$ ’ emerging from the above four axiom schemes is not of a conditional (or implication); rather, it is the relation of determination in the presence of truth-value gaps: $$\varphi \rightarrow \psi $$ is read as $$\varphi $$ determines $$\…Read more
  •  15
    Poly-Connexivity: Connexive Conjunction and Disjunction
    Notre Dame Journal of Formal Logic 63 (3): 343-355. 2022.
    This paper motivates the logic PCON, an extension of connexivity to conjunction and disjunction, called poly-connexivity. The motivation arises from differences in intonational stress patterns due to focus, where PCON turns out to be a logic of intentionally stressed connectives in focus.
  •  20
    The paper highlights proof-theoretic semantics as providing natural resources for capturing semantic variation in natural language. The semantic variations include:Distinction between extensional predication and attribution to intensional transitive verbs a non-specific object.Omission of a verbal argument in a transitive verb.Obtaining sameness of meaning of sentences with transitive verbs with omitted object and existentially quantified object.Blocking unwarranted entailments in adjective–noun…Read more
  •  11
    Logical Grounding: The Case of “if‐then‐else”
    Theoria 87 (5): 1175-1192. 2021.
    Theoria, Volume 87, Issue 5, Page 1175-1192, October 2021.
  •  19
    Logical Grounding: The Case of “ if‐then‐else”
    Theoria 87 (5): 1175-1192. 2021.
    The paper proposes grounding the ternary connective “if … then … else” (classically interpreted), thus far not considered in the logical grounding literature. In doing so, a new kind of plural grounding, called collective immediate grounding, is proposed as more adequate than the traditional complete immediate grounding in avoiding redundancy. The approach is proof‐theoretic.
  •  15
    Logical Grounding: The Case of “ if‐then‐else”
    Theoria 87 (5): 1175-1192. 2021.
    The paper proposes grounding the ternary connective “if … then … else” (classically interpreted), thus far not considered in the logical grounding literature. In doing so, a new kind of plural grounding, called collective immediate grounding, is proposed as more adequate than the traditional complete immediate grounding in avoiding redundancy. The approach is proof‐theoretic.
  •  27
    Calculi for Many-Valued Logics
    with Michael Kaminski
    Logica Universalis 15 (2): 193-226. 2021.
    We present a number of equivalent calculi for many-valued logics and prove soundness and strong completeness theorems. The calculi are obtained from the truth tables of the logic under consideration in a straightforward manner and there is a natural duality among these calculi. We also prove the cut elimination theorems for the sequent-like systems.
  •  16
    Towards a generalization of the logic of grounding
    Theoria: Revista de Teoría, Historia y Fundamentos de la Ciencia 36 (1): 5-24. 2021.
    The main goal of this paper is to provide a ground-analysis of two classical connectives that have so far been ignored in the literature, namely the exclusive disjunction, and the ternary disjunction. Such ground-analysis not only serves to extend the applicability of the logic of grounding but also leads to a generalization of Poggiolesi (2016)’s definition of the notion of complete and immediate grounding.
  •  19
    Connexive Restricted Quantification
    Notre Dame Journal of Formal Logic 61 (3): 383-402. 2020.
    This paper investigates the meaning of restricted quantification when the embedded conditional is taken as the conditional of some first-order connexive logics. The study is carried out by checking the suitability of RQ for defining a connexive class theory, in analogy to the definition of Boolean class theory by using RQ in classical logic. Negative results are obtained for Wansing’s first-order connexive logic QC and one variant of Priest’s first-order connexive logic QP. A positive result is …Read more
  •  30
    Another plan for negation
    Australasian Journal of Logic 16 (5): 159-176. 2019.
    The paper presents a plan for negation, proposing a paradigm shift from the Australian plan for negation, leading to a family of contra-classical logics. The two main ideas are the following: Instead of shifting points of evaluation (in a frame), shift the evaluated formula. Introduce an incompatibility set for every atomic formula, extended to any compound formula, and impose the condition on valuations that a formula evaluates to true iff all the formulas in its incompatibility set evaluate to…Read more
  •  38
    Proof-Theoretic Semantics for Natural Language
    Topoi 40 (1): 55-69. 2019.
    The paper has two parts: 1. A brief exposition of proof-theoretic semantics, not necessarily in connection to natural language. 2. A review, with a contrastive flavour, of some of the applications of PTS to NL with an indication of advantages of PTS as a theory of meaning for NL.
  •  25
    A Poly-Connexive Logic
    Logic and Logical Philosophy 1. forthcoming.
    The paper introduces a variant of connexive logic in which connexivity is extended from the interaction of negation with implication to the interaction of negation also with conjunction and disjunction. The logic is presented by two deductively equivalent methods: an axiomatic one and a natural-deduction one. Both are shown to be complete for a four-valued model theory.
  •  11
    De Morgan Interpretation of the Lambek–Grishin Calculus
    with Michael Kaminski
    Review of Symbolic Logic 13 (4): 845-856. 2020.
    We present an embedding of the Lambek–Grishin calculus into an extension of the nonassociative Lambek calculus with negation. The embedding is based on the De Morgan interpretation of the dual Grishin connectives.
  •  33
    On Beall’s New Interpretation of $$WK_{3}$$ W K 3
    Journal of Logic, Language and Information 28 (1): 1-7. 2019.
    I argue that a recent philosophical interpretation by Jc Beall of the middle value of Weak Kleene logic as ‘being off-topic’ is untenable. My main claim is that “being off-topic” is a relation, not a property, and as such cannot serve as an interpretation of a truth-value.
  •  18
    Structural Rules for Multi-valued Logics
    with Michael Kaminski
    Logica Universalis 13 (1): 65-75. 2019.
    We study structural rules in the context of multi-valued logics with finitely-many truth-values. We first extend Gentzen’s traditional structural rules to a multi-valued logic context; in addition, we propos some novel structural rules, fitting only multi-valued logics. Then, we propose a novel definition, namely, structural rules completeness of a collection of structural rules, requiring derivability of the restriction of consequence to atomic formulas by structural rules only. The restriction…Read more
  •  33
    Bilateralism, Trilateralism, Multilateralism and Poly-Sequents
    Journal of Philosophical Logic 48 (2): 245-262. 2019.
    The paper introduces the formula structure of poly-sequents, allowing the expression of poly-positions: positions with any number of stances, of which bilateralism and trilateralism are special cases. The paper also puts forward the view that s-coherence of such poly-positions can be defined inferentially, without appealing to their validity under interpretations of the object language.
  •  10
    Diversification of Object-Languages for Propositional Logics
    Journal of Logic, Language and Information 27 (3): 193-203. 2018.
    I argue in favour of object languages of logics to be diversely-generated, that is, not having identical immediate sub-formulas. In addition to diversely-generated object languages constituting a more appropriate abstraction of the use of sentential connectives in natural language, I show that such language lead to a simplifications w.r.t. some specific issues: the identity of proofs, the factual equivalence and the Mingle axiom in Relevance logics. I also point out that some of the properties o…Read more
  •  28
    On harmony and permuting conversions
    Journal of Applied Logic 21 14-23. 2017.
    The paper exposes the relevance of permuting conversions (in natural-deduction systems) to the role of such systems in the theory of meaning known as proof-theoretic semantics, by relating permuting conversion to harmony, hitherto related to normalisation only. This is achieved by showing the connection of permuting conversion to the general notion of canonicity, once applied to arbitrary derivations from open assumption. In the course of exposing the relationship of permuting conversions to har…Read more
  •  15
    A Proof-Theoretic Semantics for Exclusion
    with Michael Kaminski
    Logica Universalis 11 (4): 489-505. 2017.
    The paper provides a proof-theory for a negative presentation of classical logic based on a single primitive of exclusion, generalizing the known presentation via the binary ‘nand. The completeness is established via deductive equivalence to Gentzens NK/LK systems.
  •  20
    Bilateralism in Proof-Theoretic Semantics
    Journal of Philosophical Logic 43 (2-3): 239-259. 2014.
    The paper suggests a revision of the notion of harmony, a major necessary condition in proof-theoretic semantics for a natural-deduction proof-system to qualify as meaning conferring, when moving to a bilateral proof-system. The latter considers both forces of assertion and denial as primitive, and is applied here to positive logics, lacking negation altogether. It is suggested that in addition to the balance between introduction and elimination rules traditionally imposed by harmony, a balance …Read more
  •  7
    On Semi-Fusions and Semi-Negations
    SOUTH AMERICAN JOURNAL OF LOGIC 2 (1): 109-118. 2016.
  •  49
    E-Type Pronouns, I-Sums, and Donkey Anaphora
    with Shalom Lappin
    Linguistics and Philosophy 17 (4): 391-428. 1994.
  •  187
    Proof-theoretic semantics for a natural language fragment
    with Roy Dyckhoff
    Linguistics and Philosophy 33 (6): 447-477. 2010.
    The paper presents a proof-theoretic semantics (PTS) for a fragment of natural language, providing an alternative to the traditional model-theoretic (Montagovian) semantics (MTS), whereby meanings are truth-condition (in arbitrary models). Instead, meanings are taken as derivability-conditions in a dedicated natural-deduction (ND) proof-system. This semantics is effective (algorithmically decidable), adhering to the meaning as use paradigm, not suffering from several of the criticisms formulated…Read more
  •  63
    The paper proposes a semantics for contextual (i.e., Temporal and Locative) Prepositional Phrases (CPPs) like during every meeting, in the garden, when Harry met Sally and where I’m calling from. The semantics is embodied in a multi-modal extension of Combinatory Categoral Grammar (CCG). The grammar allows the strictly monotonic compositional derivation of multiple correct interpretations for “stacked” or multiple CPPs, including interpretations whose scope relations are not what would be expect…Read more
  •  58
    Plurality and temporal modification
    with Ron Artstein
    Linguistics and Philosophy 29 (3). 2006.
    A semantics with plural entitles and plural times accounts for cumulative relations between plural arguments and temporal expressions. The semantics equips nominal, verbal and sentential meanings with temporal context variables and treats temporal modifiers as temporal generalized quantifiers; cumulative conjunction, however, takes place at types lower than generalized quantifiers. The mediation of temporal context variables allows cumulative relations to percolate between an argument in a main …Read more
  •  24
    A Lambek Automaton
    with Tatyana Veksler
    Logic Journal of the IGPL 14 (5): 659-708. 2006.
    We define an automata-theoretic counterpart of grammars based on the Lambek-calculus L, a prominent formalism in computational linguistics. While the usual push-down automaton has the same weak generative power as the L-based grammars , there is no direct relationship between the computations of a PDA for some language L and the derivations of an L-based grammar for L. In the Lambek-automaton, on the other hand, there is a tight relation between automaton computations and grammar derivations. Th…Read more
  •  55
    Unification grammars and off-line parsability
    with Efrat Jaeger and Shuly Wintner
    Journal of Logic, Language and Information 14 (2): 199-234. 2005.
    Unification grammars are known to be Turing-equivalent; given a grammar G and a word w, it is undecidable whether w L(G). In order to ensure decidability, several constraints on grammars, commonly known as off-line parsability (OLP), were suggested, such that the recognition problem is decidable for grammars which satisfy OLP. An open question is whether it is decidable if a given grammar satisfies OLP. In this paper we investigate various definitions of OLP and discuss their interrelations, pro…Read more